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Sample of 16 employed American men, 40 years of age,was drawn at random: Each was asked how many hours he had watched television during the preceding week. The answ...

Question

Sample of 16 employed American men, 40 years of age,was drawn at random: Each was asked how many hours he had watched television during the preceding week. The answers listed below:Construct a box plot; (b) Draw dot diagram (c) Find the mean using actual data_ (10 points)

sample of 16 employed American men, 40 years of age,was drawn at random: Each was asked how many hours he had watched television during the preceding week. The answers listed below: Construct a box plot; (b) Draw dot diagram (c) Find the mean using actual data_ (10 points)



Answers

Hours Working A random sample of 25 college students was asked, "How many hours per week typically do you work outside the home?" Their responses were as follows:
(FIGURE CAN'T COPY)
Determine the shape of the distribution of hours worked by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes hours worked?

Mhm. Okay. So in this data if you look at that sample set it's pretty skewed it's not symmetrical. Um It looks like witches teeth actually. And there's the measurement of the meeting and the mean. Now the closer the meeting and the men are, the more symmetrical it is for our data that's pretty far apart. It's skewed therefore the median is a better used for us.

On this problem. We're talking about overtime hours, and we want to construct a probability distribution. And in order to construct a probability distribution, we need to know first the total number of employees that the company has and sort of find the total. We add up all the role, all the values in the road for employees with six plus 12 plus 29 lost, 57 plus 42 plus 30 plus 16. And that's 192. And so the probability of zero overtime hours. It's six over 192. Okay, and that's 1/32. The probability of one is 12 over 192 just 1/16. Probability of to is 29 over 192. Probability of three. That's 57 over 192 which is 19/64. Okay, probability of four. It's 42 over 192 which is 7/32. Probability of five is 30 over 192. Yeah, just 5/32 when the probability of sex yeah, is 16 over 192 which is 1/12 it's gonna make our probability distribution from this. Well, yeah. No. He said the probability of six was 1/12. Probability, five was 5/32. Probability of four was 7/32. Probability of three. 19/64. Probability of two is 29/1 92. Yeah, probability of one is 1/12. Sorry. 1/16. The probability of zero is 1/32. And so here is our probability distribution. Yeah. Does it make our history, Graham? From this, it's put X. Let's put P. Let's hear. Since we have zero. 123 four, five and sit. The one that was the biggest as we conceive from our probability distribution was three. So three will be the largest. The next largest is four and then five and then to and then six and then one in zero on. So this is what our distribution looks like. That's why, as we can see, this is slightly skewed left. Okay,

46 which distribution should use for this problem in this case were given an average of 151 and we're in a standard deviation that's representative of the sample instead of the population. Because we're given this, the distribution we should use is a T distribution.

All right. We're given information about the number of hours Americans spend watching television. The mean eyes 15 and standard errors. Four were given a simple random sample of 60 Americans. And we're supposed to find the probability that ah, we are within one hour of the population mean with but this sample mean and then 45 minutes from the population mean, which is 450.75 hours. All right. Uh, thes both have the same standard error for our population. Used are formulaic. So that's gonna be four over route 60. This is equal to about 0.516 All right, now, we can delve into these problems properly. We're gonna find our Z lower the upper usual. So that's gonna be negative. One over 0.516 and one over zero point 516 difference from the mean over the standard deviation. Uh, this would equal negative 1.94 in 1.94 If we look at our table, we get that our probability lower equals 0.0 26 to the upper probability is 0.9738 Find a probability we subtract probability upper minus probability lower. And you get 0.9476 All right, same process for part B. Except in the numerator. We're gonna have negative 7.75 and positive. 0.75 So are ze lower now is negative. 1.45 There's the upper. It's gonna be 75 over 0.516 which he calls positive. Important for 45 Right. Looking at her table, we know that our probability lower is 0.735 probability upper equals 0.9265 Ah, Subtracting p equals P U minus P l because equals 0.8530 and there you have it.


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