A population of values has a normal distribution with \mu=13.2 and \sigma=5.

shadsiei 2020-12-06 Answered

A population of values has a normal distribution with μ=13.2 and σ=5. You intend to draw a random sample of size n=60.
Find the probability that a sample of size n=60 is randomly selected with a mean between 11.5 and 14.
P(11.5<M<14)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

joshyoung05M
Answered 2020-12-07 Author has 97 answers

The probability that mean value is between 11.5 and 14 is 0.8884, which is obtained below:
P(x1<X<x2)=P(x1μσn<z<x2μσn)
P(11.5<X<14)=P(11.513.2560<z<1413.2560)
=P(2.636<z<1.240)
=P(z<1.240)P(z<2.636)[Use standard normal table]
=0.892510.00415=0.8884.

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