Question

A small shop sells a variety of smartphones. Suppose we know that the battery life of Smartphone A is normally distributed with a mean of 15 hours and a standard deviation of 6.4. Also suppose we know that the average battery life of Smartphone B is 12 hours with a standard deviation of 4.2. We know that Smartphone C has the greatest standard deviation of battery life of 7.5. Twelve hundred of the four thousand customers of the shop use Smartphone A. Seven hundred fifty of the customers use Smartphone B. 1.1. If we choose 16 Smartphone A users, what is the probability that their mean battery life will be between 14.5 and 17 hours?

Answer 1

Answer:

0.5161

Step-by-step explanation:

There is a lot of unnecessary information in this question.  We only need info for Smartphone A users since our sample size consists of entirely Smartphone A users, and it's asking about them.  So ignore any info that isn't about Smartphone A users.

We have (for Smartphone A users):

x = 15, s = 6.4, n = 16

We want:  P(14.5 < x < 17)

We need to find the z-scores for the values of 14.5 and 17 using the data for smartphone a users.  

See attached photo for the calculation of the 2 z-scores and the probabilities