Question

The lifespan of brand A batteries is Normally distributed with a mean of 108 hours and a standard deviation of 12.5 hours. The lifespan of brand B batteries is Normally distributed with a mean of 92 hours and a standard deviation of 15.1 hours. A quality-control specialist selects a random sample of 25 of each type of battery and calculates the sample mean lifespan for each brand. Let X be the difference in the sample mean lifespan for each brand of battery. What is the mean of the sampling distribution of the difference in sample means?

A) 15.1
B) 12.5
C) 3.6
D) 4.8

Answer 1

The mean of the sampling distribution of the difference in sample means is 16 hours.

Step-by-step explanation:

To find the mean of the sampling distribution of the difference in sample means, we need to subtract the mean of brand B batteries from the mean of brand A batteries. The mean of brand A batteries is 108 hours and the mean of brand B batteries is 92 hours. So, the mean of the sampling distribution of the difference in sample means is 108 - 92 = 16 hours.