Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of n=63 , find the probability of a sample mean being less than 19.8 if μ=20 and σ=1.33.

For a sample of n=63 , the probability of a sample mean being less than 19.8 if μ=20 and σ=1.33 is ______.

(Round to four decimal places as needed.)

Would the given sample mean be considered unusual?

The sample mean (would not/ would) be considered unusual because it has a probability that is (less/ greater) than 5%

Answer 1

Solution :

Given that ,

mean = = 20

standard deviation = = 1.33

n = 63

= 20 and

= / n = 1.33 /  63 = 0.16756

P( < 19.8) = P(( - ) / < (19.8 - 20) / 0.16756)

= P(z < -1.194)

= 0.1162   

Probability = 0.1162

probability > 0.05

The sample mean would not be considered unusual because it has a probability that is greater than 5% .