Question: Sampling Distribution The time to repair a computer is normally distributed with a mean of 2 hours 17 minutes and a standard deviation of 29

Sampling Distribution

The time to repair a computer is normally distributed with a mean of 2 hours 17 minutes and a standard deviation of 29 minutes. A random sample of 49 computers has been chosen.

a) Find the mean of the distribution.

b) What is the standard error for the sample mean?

c) What probability sample mean will have time to repair exactly 138 minutes?

d) What is the probability that the sample mean will have time to repair more than 145 minutes

e) What is the probability that the sample mean will have time to repair less than 135 minutes?

f) What is the probability that the sample mean will have time to repair between 130 minutes and 147 minutes?

Reference :

*Z&T Table Distribution

https://drive.google.com/file/d/1nfSbQHR6k8Ri5ipEPBM1-4ZpLiMfKsvC/view?usp=sharing

Sampling DistributionThe time to repair a computer is normally distributed with a

KEY EQUATIONS Population Mean Finding X for the Sampling Distribution of the Mean X X =u+Z- Vn (7.5) u = (7.1) N Sample Proportion Population Standard Deviation P X (7.6) E(X; - 1)2 o (7.2) Standard Error of the Proportion N TT (1 - TT) Op = (7.7) Standard Error of the Mean n Vn (7.3) Finding Z for the Sampling Distribution of the Proportion P - TT Finding Z for the Sampling Distribution of the Mean Z = (7.8) TT (1 - TT) Z = - X - MX X -M (7.4) OX Vn The sampling distribution of mean The sampling distribution of mean proportion H x = H Mean of sample proportion = p Ox = = standard error 0 = bd n => standard error For finite population, o x= V-n N-1 Probability Z = p-p p ( 1 -p ) n Probability z = x- u or z = N - n VN-1

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