Question

Suppose that it is known that if a certain tablet is fully charged and then left on,the tablet has mean battery life of 145 minutes and the standard deviation of the battery life is 17 minutes. A random sample of 55 tablets is taken.

a.Describe the shape of the sampling distribution of ?̅, the sample mean of the battery life of the tablet.Justify your answer.

b.Find the mean and standard deviation of the sampling distribution of ?̅.c.If a random sample of 10 tablets is taken, can we determine the shape of the sampling distribution of ?̅?

Answer 1

Solution :

Given that,

mean = = 145

standard deviation = = 17

n = 55

a) The shape of the sampling distribution of is approximately normal because sample size is greater than 30

b) = = 145

= / n = 17 / 55 = 2.29

c) n = 10

The shape of the sampling distribution of is normal

= = 145

= / n = 17 / 10 = 5.38