Question

A big box store sells an average of 250 laptop computers per month , with a standard deviation of 100 laptops. suppose we take a sample for 10 months. Find the probability of that the sample mean mean number of laptops is greater than 275. The distribution of laptops is normal.

Answer 1

Solution:

   We are given that: The distribution of laptops is normal with mean sells of 250 laptop computers per month, with a standard deviation of 100 laptops.

That is: and , n = number of months = 10

   We have to find the probability that the sample mean number of laptops is greater than 275.

That is:

Thus find z score:

Thus we get:

Thus to P( Z < 0.79) , look in z table for z = 0.7 and 0.09 and find corresponding area.

For z = 0.7 and 0.09 , area is 0.7852

That is: P( Z< 0.79) = 0.7852

Thus

Thus, the probability that the sample mean number of laptops is greater than 275 is 0.2148.