Question

In a recent study reported Oct 29, 2012 on the Flurry Blog, the mean age of tablet users is 34 years. Suppose the standard deviation is 15 years. Take a sample of size n = 100

a. What are the mean and standard deviation for the sample mean ages of tablet users?

b. What does the distribution look like?

c. Find the probability that the sample mean age is more than 30 years (the reported mean age of tablet users in this particular study.)

d. Find the 95?ℎ percentile for the sample mean age (to one decimal place).

Answer 1

Solution :

Given that ,

mean = = 34

standard deviation = = 15

a) =   = 34

= / n = 15 / 100 = 1.5

b) The shape of sampling distribution is approximately normal.

c) P( > 30) = 1 - P( < 30)

= 1 - P[( - ) / < (30 - 34) / 1.5 ]

= 1 - P(z < -2.67)   

= 1 - 0.0038

= 0.9962

Using standard normal table,

P(Z < z) = 95%

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95

z = 1.645

Using z-score formula  

= z * +   

= 1.645 * 1.5 + 34

= 36.5 years