In the library on a university campus, there is a sign in...

In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of $2500 \mathrm{lb}$. Assume that the average weight of students, faculty, and staff on campus is $150 \mathrm{lb}$, that the standard deviation is $27 \mathrm{lb}$, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken: a. What is the mean value of the distribution of the sample mean? b. What is the standard deviation of the sampling distribution of the sample mean weight? c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of $2500 \mathrm{lb}$ ? d. What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit?

Transcript

00:01 Hi, i'm david and i'm here to have you answer your question.

00:03 Now let me bring up your question here.

00:06 In the question here, we are going to discuss about the normal distribution.

00:10 Let me remind to you that if the x that follows by the normal, with the mean and standard division, then the sum of mean x bar also followed by the normal.

00:19 When the minimum xx equal to the mean of population, standard division x bar equal to the standard division of population, divide with square of n.

00:27 And because it follows by the normal, it will tend the xbound will minus the mean under the standard division.

00:34 We obtain the standard normal.

00:36 In the question here, we have the weight of the student x.

00:41 It will follow by the normal.

00:44 With the mean, it will equal to the 150 and the standard division equal to the 27.

00:58 We have the symbol n equals to the 16 pupil.

01:01 And in the question a, want to find the mean value of the sample mean x bar.

01:11 By the formula, it will equal to the mean of the population and equal to the 150.

01:16 For the question b, want to find the standard division of the sample mean.

01:22 So, signal of the x bar, by the formula, it will equal to the sigma over square zeta n, equal to the 27 over square rather the 16, equal to the 27 over, 4 and then we get equal to the 6 .75.

01:41 For the question c, 1 2, 1 is the avid weight on the 16 then it will be exit in the june 2500.

01:51 So we have the x bar equal to the 2 ,500 we divided by the 16 and then we get equal to the 156 .255 and for the so question d, once you find the probability that it will be exceed the weight limit, so want to find the probability in the x bar will be greater than the limit here will be the $2 ,500.

02:21 And then it means then we need to convert the x bar into this will be greater than this amount here will be the 156 .25...

Question

Please give Ace some feedback