A population of values has a normal distribution with \mu=26.8 and \sigma=33.8. Yo

ankarskogC 2020-12-15 Answered

A population of values has a normal distribution with μ=26.8 and σ=33.8. You intend to draw a random sample of size n=89.
Find the probability that a sample of size n=89 is randomly selected with a mean between 17.1 and 25.
P(17.1<M<25)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Obiajulu
Answered 2020-12-16 Author has 98 answers

Step 1
It is given that a population of values distributed normally with mean 26.8 and standard deviation 33.8. The sample size is 89.
Step 2
Calculate the probability that a sample of size n=89 is randomly selected with a mean between 17.1 and 25 is as follows:
P(17.1<X<25)=P(17.1μσn<Xμσn<25μσn)
=P(17.126.833.889<Z<2526.833.889)
P(9.73.58279<Z<1.83.58279)
=P(2.707<Z<0.502)
=P(Z<0.053)P(Z<0.287)(Using Excel functions,P(Z<0.053)=0.4789P(Z<0.287)=0.3871)
=0.30780.0034=0.3044
Therefore, the value of P(17.1<M<25)=0.3044.

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