Question

A population is known to have a mean of 10 and a standard deviation of 1.1. A sample of size 32 is randomly selected from the population.

a. What is the probability that the sample mean is less than 9.9?

b. What percent of the population is greater than 10.2?

c. What’s the probability that the sample mean is greater than 10.5?

Answer 1

a, Here sample size is 32, so as per central limit theorem distribution of sample mean is normal with mean=10 and standard deviation is

Now we need to find

As distribution is normal we can convert sample mean to z

b. Now we need to find

c. Now we need to find