Question

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A. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 95% of all sample means will fall between what two values?

B. Salmon weights are bell-shaped, with a mean of 12.3 pounds and standard deviation of 2 pounds. According to the Empirical Rule, approximately 95% of all salmon weigh between what two values?

Answer 1

A) We are given here the distribution as:

Using the Central limit theorem, the distribution of the sample mean of sample size n = 16 is given here as:

From standard normal tables, we have:
P( -1.96 < Z < 1.96) =0.95

Therefore the lower and upper limits here are computed as:
L = Mean - 1.96*SD = 45 - 1.96*2.5 = 45 - 4.9 = 40.1
U = Mean + 1.96*SD = 45 + 1.96*2.5 = 49.9

Therefore 40.1, 49.9 is the required range here.

b) We are given the distribution here as:

According to empirical rule, 95% of the observations lies within 2 standard deviations of the mean. Therefore the limit here is computed as:

12.3 - 2*2 to 12.3 + 2*2

8.3 to 16.3

This is the required range of values here.