A population of values has a normal distribution with \mu=26.8 and \sigma=33.8. You intend to draw a random sample of size n=89.

waigaK 2020-10-20 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 single randomly selected value is between 17.1 and 25.
P(17.1<X<25)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

averes8
Answered 2020-10-21 Author has 92 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 single randomly selected value is between 17.1 and 25 is as follows:
P(17.1<X<25)=P(17.1μσ<Xμσ<25μσ)
=P(17.126.833.8<Z<2526.833.8)
=P(0.287<Z<0.053)
=P(Z<0.053)P(Z<0.287)P(Z<0.053)=0.4789P(Z<0.287)=0.3871)
=0.47890.3871=0.0918
Therefore, the value of P(17.1<X<25)=0.0918.

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