5

ForechoL thgremining qucstions_Youued Niiteme ptobabilit euemcnttont Wxu oue wihEshade gruph undincludeyur culculater_commnd JusLllikewedid inchssWe are told data s...

Question

ForechoL thgremining qucstions_Youued Niiteme ptobabilit euemcnttont Wxu oue wihEshade gruph undincludeyur culculater_commnd JusLllikewedid inchssWe are told data sct has mean of 98 and standard deviation of 21.Find the probability > < 75duoidonFind the probability * > 69ea eo-1' (-0l aanid ) 2o JnjVu FTw2 4t bjebianc? 4un6 'EI [ ( Bvd Jenb o cc ludiuaib vlleariea 2nnb Jns;: 907v; )i, Silh F boletain *1 LaEm &/bl-Tu Molli 1* eldat Momyint Sde {90#Find the probability 69 &l

ForechoL thgremining qucstions_Youued Niiteme ptobabilit euemcnttont Wxu oue wihEshade gruph undincludeyur culculater_commnd JusLllikewedid inchss We are told data sct has mean of 98 and standard deviation of 21. Find the probability > < 75 duoidon Find the probability * > 69 ea eo-1' (-0l aanid ) 2o JnjVu FTw2 4t bjebianc? 4un6 'EI [ ( Bvd Jenb o cc ludiuaib vlleariea 2nnb Jns;: 907v; )i, Silh F boletain *1 LaEm &/bl-Tu Molli 1* eldat Momyint Sde {90# Find the probability 69 < x < 75 3n34 Ulinb #dK Vulidnd , Iblib ei 0 Ino (this problem continues on the next page) The length of time it takes t0 find parking space at 9 AM. follows normal distrib with & mean of five minutes and standard deviation of nwo minutes: (Illowsky; p words define the random variable X Based upon the given information and numerically justified, would you be surp took less than one minute to find a barking snace?



Answers

Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and
a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~ _____(_____,_____)
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

74 i Q is normally distributed with the mean of 100 a standard deviation of 15. Supposed one individual is randomly chosen. Let X because you are an individual. Hey, X could be mined by human evolution. Flip mean 100 a center deviation of 15 Be Find the probability that the person has an I Q. Greater than 1 20 All right, that is 1 20 included photograph and write a probability statement. So have a probability statement. Uh, quick sketch where I want to mark the mean and I want to do obscenity vision on each side of that. My boundary value of the value that I'm looking at here is 1 20 and I want to know the probability greater than 1 20 In order to stop that, I can use my normal CDF function calculator. Ah, lower bound. Here was the 1 20 My upper bound was infinity. But understand certain 9999 mean ended up being 100 center deviation was 15. I can play that in to find my very small area 0.0 in on 12 say small because I could see my graph that it's a small area that I shaded in. So my answer, my picture should, um, be similar. See, kill me in S A is an organization whose members have the top 2% of all accuse. Find a minimum. I Q needed to qualify for this organization and sketch the graft. So want to think about what's going on here, in which we have 100 as the center and the standard deviation being 15. So this is organization, which they contain the top 2% of all IQ's. I want to find that minimum value because I'm looking for that minimum value and looking for this little boundary about you that separates the left side of the draft from the right side of Well, in order to figure this out, I want to focus on the left side of this information because generally your calculators are left side functions. So the area to the left of this bulan has actually point not eight. So I'm looking for here's which value in which X is less than K K is gonna be. My mystery value gives us an area of 0.98 So there's my probability statement in order to solve this invert norm feature in which I answered the area to the left area to the left 0.98 Here the mean is 100 the standard deviation is 15. Tanaka found that boundary value to be 130.8 d the middle, 50% of all I used ball between which to values sketched the graph and rightly probability statement. I know that have a mean of 100 Senate aviation 1 15 and I want to figure out that the middle 50% fall between which to values. Well, in this case, I'm gonna treat you like a separate process. Um, because I can use my inverse norm calculator function too soft for this. Um, I can solve for my first question, Mark, I'll call this question mark number one, and then I could solve for question mark number. So my probability statements to help me answer these for question mark number one. Essentially, we're looking for where the probability where X is less than okay. One to equal. So you think the area with left because my calculators left side function here? Uh, the area to the left of this value is 25 because I have a symmetrical distribution with 50% in the middle. I have 25 1 that left have 25 on the right because into higher curve equals one. So the first thing I'm looking for here is which value gives me an area 25 so I can use my inverse norm. A 0.25 my area Mean was 100. My standard deviation. 15. This gives me 89.88 So I have my first value. And then from our second value, I think about this question number two, the total area to the left of that I used actually 75%. So it'll look like probability. That X is less than Kate, too. Would be £0.7. So my inverse norm statement will look very similar. Except I'll insert of 75 for my area and I'll get a value of 1 10.12

73. According to a study done by Day Anza students, the height for Asian adult males is normally distributed with an average of 66 inches in a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X equal the height of the individual. Hey, X is gonna follow normal distribution. We're gonna have a means of 66 in a standard deviation of 2.5. Be find the probability that the person is between 65 69 inches. So want to find the probability that the person is between 65 at 69 inches, include a sketch of the craft and write a statement. So a quick sketch in which were centered at 66? Well, we have a standard deviation of 2.5. I want to find the probability that an individual is completed 65 inches and 69 inches. So this shaded region I can use my normal CDF command here. My calculator, my lower bound in this case would be 65 my upper bound would be 69. Um, I mean 66 with a 2.5 standard deviation I don't get an area of point 5404 I see. Would you expect to meet many Asian adult males over 72 inches? Explain why, Why not justify your answer? Well, we want to figure out what is the probability that an Asian adult male is over 72 inches. So using the same type of space above where we have a center of 66 and the standard deviation 2.5. We know that 72 somewhere over here, to the right shaded regions to write. So based on the picture, we know that the probability is small, but let's determine how small it is we can use. Our normal CDF demand, which were lower bound, is where we started to shade, which is 72. This goes to infinity, so even represent that with 999 we have a mean of 66 a standard deviation of 2.5. We get the probability of 0.8 So would you expect to me mediation adult males over 72 inches? To my way of saying no sense, the probability of an Asian adult male being taller? 72 inches. It is very low, and I'll share the prince ese and the probability

71 finding the probability that it takes at least eight minutes to find a parking spot. So we have this normal distribution, I mean, of five Senate deviation to own it, on the probability that it takes at least eight minutes to find a parking spot, which is the road. But X is greater than eight. So I can use my normal CDF function here. I want to start a eight and I'm interested in all values above it. So I'm gonna go from eight to infinity and have infinity as a key for my calculator. Second insert? None None. None have a mean of five a standard deviation too. And get a probability of 0.668 which is option d.

In this question, we're told that there is a ballpark. And before a game, vehicles arrived into the ballpark parking lot from the West Side with a rate of 10 per minute and from the east side with a rate of 15 per minute. And we're also told that these arrivals on each side of the parking lot are porcelain processes that air independent from each other. Now, the thing that this question touches on and tries to teach us about is the additive properties of porcelain processes. So if you have two independent person processes, you can characterize them by summing them to create a third process. That is, if they're independent. So for cars entering on the west side of the parking lot, the number of cars that arrive in a given amount of time is a personal random variable, and it has a mean parameter of Lambda Times T or 10 times T and likewise from the east side of the parking lot. The number of cars that arrive in a given amount of time is also a person with mean Lambda Times T or 15 times T. Now we can define a third personal random variable which is the sum of the two first ones since their independence. So we could say that there's some is equal to some third personal random variable. And we can also say that the arrival rate for the third one is equal to the sum of the arrival rates for the first two. So therefore, the total number of arrivals in a given amount of time is also I put some around a variable, but it has a mean of 25 t, and now we can get into the business of answering the questions. So for part, A were asked what the expected number of cars that entered the parking lot in any 10 minute span is, and what is the corresponding standard deviation. So for looking at the total number of cars entering in 10 minutes, we can use this random variable and the mean for put some random variable is equal to Lambda Times T, and in this case, it's Lambda is 25 T is 10 minutes, so we have 250. So 250 is the expected number of cars that enter the parking lot in total in the 10 minute spin now for a Poisson random variable. The variance is also equal to the main, so therefore, the standard deviation of the number of cars that arrive in a 10 minute span is equal to the square root of 250 and that comes out to you 15.81 Yeah, now for Part B were asked that what is the probability that in any particular minute that exactly 12 cars enter from each side? So for this question, it is easier to decompose it back into the two separate possum processes. So the car is entering from the west side and the car is entering from the east side. So we're looking for the probability that number of cars that enter in one minute from the West side is equal to 12, and the number of cars that enter from the East Side in one minute is also equal to 12. And because these are independent personal processes, this probability is equal to the product of the probabilities of each of these events occurring separately. So that's the probability that X one in one minute is equal to 12 times the probability X two in one minute is equal to 12 now, Unlike party, which was a duration of 10 minutes, this is a duration of one minute. So the mean for the first process is 10 times one, and the mean for the second process is 15. So we could say that the probability is equal to you E to the negative 10 times 10 to the exponents, 12 over 12 factorial times e to the negative 15 times 15 to fix opponent 12 over 12 factorial and this comes out to approximately 0.8 So the probability that exactly 12 cars come in from each the west and the east side of the parking lot in a one minute spin is 0.8 Now, for part C, we're asked, what is the probability that exactly 24 cars enter the lot in any particular moment? So this is the total number of cars entering the lot, and we know that the combined rate is 25 t is equal to one minute. So this is a put some random variable with mean lambda three times t. It was 25 and so we're looking for the probability that the total number of arrivals in one minute is equal to 24. This is equal thio e to the negative 25 times 25 to the exponents, 24 over 24 factorial, and this comes out to about zero point 080 So the probability that exactly 24 cars arrive in any given minute is 0.8 And finally, for part D were asked to write an expression for the probability that in any given minute the same number of cars enter enter through both the east and the west sides of the parking lot. So this is just the probability that the number of cars arriving as a result of the first process is equal to the number of the car is arriving as a result of the second process. And keep in mind that we have to plus, um, a random variables here. So the first one has mean so this is one minute, so it has a mean of 10, and the second process has a mean of 15. So this is the probability that both x one and X two are equal. So this is the probability that both X one and X two equals zero, plus the probability that both x one and X two equal one, plus the probability that both x x one and X two equals three and so on. So we can write this as so. It's this summation up to infinity. So there is no upper bound on the number of events that occur as a result of a person process. And the reason why I am multiplying these probabilities is because the two processes are independent processes. Now we can write this using this summation notation. So for X from zero to infinity probability, that number arriving as a result of process one in one minute is equally x times the probability that the number arriving as a result of process to in one minute is also equal to X. And this is equal to the summation of the following. And we can simplify this a little bit. So we have e to the minus 25 and come out of the summation. So this is simplified to 152 the Exponents X and it's expect Auriol squared. And so there may be some fancier ways to simplify this or express it differently. But this is indeed an expression for the probability that in any given minute the same number of cars entered through both sides of the parking lot.


Similar Solved Questions

5 answers
McusWic thc timc Vecellarlons From thc Uimc cakubtc tha pcriod For scvcmi cllaciimnesc = tcquen_ id nnwulIr Inyucag Do nof calculeictutfre mandm0;4F 0ACa T 145iof ) =r CD @ ENnr ucu difticult deletninclooking u the prpt Licl ocly (Usc kg idantttie sinplify-) Mfyou Erph logly) = k2lxk #hal heshnnc? #hat is tkasp' Usizg Excel, crale dala columns for ke(e)) und loglmL Ccalc grph of log(m) KKie logta) (#-atis) (Usc the kr dL nLbanlue! Whil Gn?U dt4s ThnG
mcusWic thc timc Vecellarlons From thc Uimc cakubtc tha pcriod For scvcmi cllaciimnesc = tcquen_ id nnwulIr Inyucag Do nof calculeictutfre mandm 0;4F 0A C a T 145i of ) =r CD @ ENnr ucu difticult deletninc looking u the prpt Licl ocly (Usc kg idantttie sinplify-) Mfyou Erph logly) = k2lxk #hal heshn...
5 answers
Score: 0 of 1 pt8 of 9 (5 complete)5.5.53Solve the following logarithmic equation_log (Zx + 1) - log (x- 3) =1Select the correct choice below and, if necessary; fill in the answer box:OA The solution is X = (Type an integer or a simplified fraction ) The solution is not a real numberClick to select and enter your answer(s) and then click Check Answer:
Score: 0 of 1 pt 8 of 9 (5 complete) 5.5.53 Solve the following logarithmic equation_ log (Zx + 1) - log (x- 3) =1 Select the correct choice below and, if necessary; fill in the answer box: OA The solution is X = (Type an integer or a simplified fraction ) The solution is not a real number Click to ...
5 answers
2 Find the variance for the scores in the following data set: 90, 89, 82, 87,93,92,98, 79,81,80. Show that the sum of the deviations is Zero.2. Find the standard deviation from the variance in Exercise 22_
2 Find the variance for the scores in the following data set: 90, 89, 82, 87,93,92,98, 79,81,80. Show that the sum of the deviations is Zero. 2. Find the standard deviation from the variance in Exercise 22_...
5 answers
An object is placed 30 cm from a screen: At what ppoints between the object and the screen can a lens of focal length 5 cm be placed to obtain an image on the screen?
An object is placed 30 cm from a screen: At what ppoints between the object and the screen can a lens of focal length 5 cm be placed to obtain an image on the screen?...
5 answers
IXON (H Jamsuv 4204j 0 Uomnios KBla dn annsnolnalcIuH 8.0'u(z) 18J4 HO "ouwx(e)"UoipeaJ Bbeaeap? ONePIXO buimolag B41 JOJ 'Japjo Jay1a Ul 'spnpojd pauoo 841 Mejo
IXON (H Jamsuv 4204j 0 Uomnios KBla dn ann snolnalc IuH 8 .0'u(z) 18J4 HO "ouwx(e) "UoipeaJ Bbeaeap? ONePIXO buimolag B41 JOJ 'Japjo Jay1a Ul 'spnpojd pauoo 841 Mejo...
5 answers
The following carbocation is foned as intenediale during dehydration reaction of an alcohol. What are thc possible alkene products that can be formed (rom this" Which one will be the major product? (7 pts). (Note: mechanism notasked)Using energy dingrams explain why the SNZ reaction of CH CH CHBr with NaOH Aastet DMSO.inslead of walet, used 4 tic solvent pU)
The following carbocation is foned as intenediale during dehydration reaction of an alcohol. What are thc possible alkene products that can be formed (rom this" Which one will be the major product? (7 pts). (Note: mechanism notasked) Using energy dingrams explain why the SNZ reaction of CH CH C...
5 answers
Box plot of Calories8
Box plot of Calories 8...
5 answers
Question 81.5 ptsCyanobacteriaNostoc; live cultureNostoc cSpecialized cells of this organism; calledwill fix atmosphericto produce amino acids and nuclelc acids: Other specializedcells calledare resting cells that serve as survlval structures-
Question 8 1.5 pts Cyanobacteria Nostoc; live culture Nostoc c Specialized cells of this organism; called will fix atmospheric to produce amino acids and nuclelc acids: Other specialized cells called are resting cells that serve as survlval structures-...
5 answers
What are the best dietary sources of calcium, phosphorus, and cobalt?
What are the best dietary sources of calcium, phosphorus, and cobalt?...
5 answers
[-71 Points]DSTAISERCPIOHteeoACur TeaCHE?Urciont (rlnhos17710locomobae conatant pJI CleaNFot IonaMnJIEtnn Wnncet[DAmh?Maale
[-71 Points] DSTAI SERCPIO Hteeo ACur TeaCHE? Urciont (rlnhos 17710 locomobae conatant pJI Clea NFot Iona MnJI Etnn Wnn cet[D Amh? Maale...
5 answers
An enzyme, a tumor suppressor gene and an oncogene meet bychance in a bar… and after a short round of introductions they soonrealize that they are each likely to be the most biologicallyimportant member of their respective protein class - at least as itrelates to cellular transformation. They are: a. Histone kinase,p53 and Rb. b. Rb, hexose kinase and ras. c. Telomerase, p53 andras. d. p53, Rb and telomerase.
An enzyme, a tumor suppressor gene and an oncogene meet by chance in a bar… and after a short round of introductions they soon realize that they are each likely to be the most biologically important member of their respective protein class - at least as it relates to cellular transformation. T...
5 answers
Let X be a binomial random variable with n trials and probability of success p. In which one of the following situations is the normal approximation to the binomial distribution most appropriate?Select one:a.n = 200, p = 0.98b.n = 1000, p = 0.001c.n = 100, p = 0.02d.n = 500, p = 0.01e.n = 50, p = 0.8
Let X be a binomial random variable with n trials and probability of success p. In which one of the following situations is the normal approximation to the binomial distribution most appropriate? Select one: a.n = 200, p = 0.98 b.n = 1000, p = 0.001 c.n = 100, p = 0.02 d.n = 500, p = 0.01 e.n = 50, ...
5 answers
Problem 3: Electrophilic Additions Give the major product of the following reactions.I,SO,H,o1) Hg(OAc) , H,ONaBH;PaBaSOaNa / NH,1) 0,, CH,CL 2) DMS
Problem 3: Electrophilic Additions Give the major product of the following reactions. I,SO, H,o 1) Hg(OAc) , H,O NaBH; PaBaSOa Na / NH, 1) 0,, CH,CL 2) DMS...
5 answers
2. Find a solution for the differential equation. (e"+ e *) dy=y dx
2. Find a solution for the differential equation. (e"+ e *) dy=y dx...
4 answers
Problem 5 (2Opts): Solve the Laplace equation on a sphere of unit radius with a boundary condition given by f (x) 20 (cos 0 + 1)
Problem 5 (2Opts): Solve the Laplace equation on a sphere of unit radius with a boundary condition given by f (x) 20 (cos 0 + 1)...

-- 0.023866--