Question

A population of values has a normal distribution with μ=51.6 and σ=87.7 You intend to draw a random sample of size n=35

Find the probability that a sample of size n=35 is randomly selected with a mean between 69.4 and 90.1

P(69.4 < M < 90.1) = ________

I tried using excel, kept on getting an error. My calculator doesn't have the "Normalcdf command" any help will greatly be appreciated, also a calculator recommendation will be appreciated as well, thank you.  

Answer 1

Population parameters of X are μ=51.6 and σ=87.7

As per CLT, if the sample size, n is greater than or equal to 30, we can use a normal distribution for Mean of X, and

or M follows a normal distribution with mean = 51.6 and Standard deviation =

M ~ N(51.6, 14.824)

We need to find P(69.4 < M < 90.1)

P(69.4 < M < 90.1) = P(M<90.1) - P(69.4)

= NORM.DIST(90.1, 51.6,14.824,1) - NORM.DIST(69.4, 51.6,14.824,1)

= 0.9953 - 0.885077

= 0.1102

So, the answer is 0.1102

I have used Excel to calculate the probability. Please let me know if you have any doubts. Happy to help. Please thumbs up if you like the solution. Thanks