A population of values has a normal distribution with mean 18.6 and standard deviation 57. If a random sample of size n=25 is selected, Find the probability that a sample of size n=25 is randomly selected with a mean greater than 17.5 round your answer to four decimal places. P=?

BolkowN 2020-11-08 Answered
A population of values has a normal distribution with mean 18.6 and standard deviation 57. If a random sample of size n=25 is selected,
Find the probability that a sample of size n=25 is randomly selected with a mean greater than 17.5 round your answer to four decimal places.
P=?
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Expert Answer

Isma Jimenez
Answered 2020-11-09 Author has 84 answers

A population of values has a normal distribution with mean 18.6 and standard deviation 57, sample size is n=25. The value of x is 17.5. The z-score is,
z=x-μσn
=17.5-18.65725
=-1.111.4=-0.0965
The area to the right of z=0.0965 under the standard normal curve is Pz>0.0965=1Pz<0.0965
The probability of z less than 0.0965 can be obtained using the excel formula “=NORM.S.DIST(0.0965,TRUE)”. The probability value is 0.4616.
The probability that a sample of size n=25 is randomly selected with a mean greater than 17.5 is,
Pz0.0965=1-Pz<-0.0965
1-0.4616=0.5384
Thus, the probability that a sample of size n=25 is randomly selected with a mean greater than 17.5 is 0.5384.

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