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Ahnual salarles Of pharmaclsts are normally distributed With the middle 97% + pharmacists earning between $82,961,00 and $112,039.00, Standard Normal Dlstrbutlon Ta...

Question

Ahnual salarles Of pharmaclsts are normally distributed With the middle 97% + pharmacists earning between $82,961,00 and $112,039.00, Standard Normal Dlstrbutlon Table What are the mean and standard deviation of the anrual salarles for pharmacIsts? Meau: SD: &

Ahnual salarles Of pharmaclsts are normally distributed With the middle 97% + pharmacists earning between $82,961,00 and $112,039.00, Standard Normal Dlstrbutlon Table What are the mean and standard deviation of the anrual salarles for pharmacIsts? Meau: SD: &



Answers

What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution?

Okay, So for this question, we want to find that the values for for our Constance see here that give us this probability. Okay, so we want to find the value. See such that the amount of probability between 54 minus c infant for four plus C is 1/2. Basically, we want to find the points here and here that are the same distance apart so that the area between is 0.5. So if we rewrite this, we considered probability that X is less than or equal to 54.4 plus C minus the probability the axe is less than or equal to 54.4 minus C is equal to 1/2. And if we go ahead and standardize both sides here, we'll get the probability that the standard Z is less than or equal to see over 13.5, minus the probability that see is less than or equal to negative. See, over the 18.5 equals 1/2. And from here, we wanna use the fact that well, first we'll copy this down. Then we want to use the fact that p probability that see, it's less than equal to negative. See, over 13.5 is equal to one minus. The probability that you see is less than or equal to positive. See over 13.5 and this is equal to 1/2. So if we distribute are negative. Uh, we'll get two times its probability. My s one equals 1/2. We had one over. We'll get three house divide by two. We'll get 3/4. So the probability that Z this lesson equal to see over 13.5 is he quoted 3/4. So it's just arithmetic from they're treating this like a variable. So then we want to go and find our normal table with the positive values and we want to locate. It's pretty tiny wants from you. We want to locate the spot where it's 3/4. So if we go and find spot where we've got 0.75 probability, the closest we can get and hands, here's 751 and here's point 7486 of this one is slightly closer. So the spot where we have 0.75 problem probabilities to the left is at 0.6 seven, So I'm gonna scroll down a little bit and we're gonna right. The probability Z is less than or equal 2.67 is equal to 3/4. So that means see, over 13.5 has equal 0.67 which means that sea has to cool 13.5 times 0.67 which is 9.0 for five and then coming back up to the top. The two values on either side of X here are gonna be 54.4 uh, minus 9.45 which gives us 45 point three six and then 54.4 plus 9.45 which gives us 63.45 And so this will be our final answer.

Four. The standard normal distribution has mean view and some Division one. This is the blue trade. This is you, uh, this is and as and you say 68% off the data and this is 95% off the data, and this is 99% off the date. So on the son of division is this is one standard the year, so the mean is equal to zero, and standard division is equal to one. This is negative three. And this is negative. Two negative one, Jew. 123

You have the date off, we clearing off weekly earning Go Union and Non Union Workers Union. I'm non union workers off different occupation. For this given data we have to calculate mean that is expert and range where to calculate mean rate and standard deviation for both union and non union workers. So first, let us take union workers here. So for union workers, let us calculate mean for so mean is given by former Other Is X Bible because toe submission or fix that is information of the given data dared by the number off occupation that is in. So we'll get the value as summation up. This given well weekly income will because to 4 4085 dared by the number off occupation years summit. So we'll get the mean value as 6 40.7 So when we around this value, so we'll get them mean for this union workers as 6 41 So this is the answer For the first part. No second parties range where to find so range we have a formula for in that is greatest value. Greatest value in the off the income miners least value of the income. So in the income in the union working class that in union working class we can see that construction occupation is having greater sin. Cos so range will be closed toe 7 78 miners least income is from the trade that is for 99. So we'll get the range as to 79. So this is the range for the first union class now coming to standard division off Union class. That is sick month. So Sigma, the other formula is squared off. Summation off X minus X bar. The old square where expertise the mean divided by the number off occupation. So once upsetting the values will get this s square it off. 6000 69 66,022 donated by seven because number off occupation is seven. So we'll get this as 97.77 So when we around, this value will get The standard division has 98. So we got mean grains and standard deviation for union working class. Now coming to nonunion working class, that is we are to find mean again nonunion working class so mean that is ex Bible because two using the same formula that is summation off exterior by, and we'll get this asked. Permission off X is 9 3050 That is a summation off the income off the seven occupation. Do it by the total number of occupation in non union, also seven. So this will be caused to 5 64.2 So when we around this value so we'll get the mean as Fight 64 know where to find range for non union, so range will be caused to same formula that is greatest value when it's least value. So in Long Union the iest artilleries mining, which is 7 35 and the least arteries bread that is 40 80. So we'll get the Rangers 317 year. So this is the range now. The last part of the question is where to find standard deviation for non union that is standard division, the same formula. What we use previously for the union that a sig Marvel week was two square root off summation off X minus expert. The old square dirtied by the number off occupation, their expertise that mean so on sub shooting the values will get. This has 67 59,080 dared when number off occupation is seven. So we'll get decides square root off 8000 final and 16.85 So which is it close to 92.28? So that is around this value. So that is 92. So we'll get the standard deviation as 92 years. So this is the answer for this given caution.

Here we have to find mean That is expert and standard deviation that is Sigma for the given set of values. So this to all the unknowns here. So let us find first mean like let us first find the meat so mean expert will be closed toe. So this is given a summation off the given set of values. They would bite portal number of values. So on substituting the values he ever get the summation off the given set of values will be caused to one yet 10 dared by the total set, the total number of values in the given cities seven year have seven set of values. So on dividing 1810 by seven will get answered us to 58 0.57 so we can round this off too. So we'll get the mean values to 59. So this is the mean man, you that is expert. So this is the answer. The first part of the answer now coming to second part of the answer that is where to find the standard deviation you. So standard deviation is given by formula that is quite right. Off summation off X minus expert, The old square divided by the number of times that is in so on, substituting the values here we'll get the standard deviation as it caused too. So this will be construed to 28 point 34 So we can around this value too. So we'll get the signal value, which will be the standard divisional because to 28. So this this is the answer for the given question that is that mean is 2 59 and the standard deviation is tough to 28.


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