A population of values has a normal distribution with \mu=29.3 and \sigma=65.1. You intend to draw a random sample of size n=142.

amanf 2020-11-30 Answered

A population of values has a normal distribution with μ=29.3 and σ=65.1. You intend to draw a random sample of size n=142.
Find the probability that a sample of size n=142 is randomly selected with a mean between 27.7 and 35.3.
P(27.7<X<35.3)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Bertha Stark
Answered 2020-12-01 Author has 96 answers

Step 1
According to the provided information,
μ=29.3
σ=65.1
n=142
P(27.7<X<35.3)=P(27.729.365.1142<Xμσn<35.329.365.1142)
=P(0.29<Z<1.1)(Z=Xμσ)
=0.4784 (From standard normal table)
Therefore, the probability that a sample of size n=142 is randomly selected with a mean between 27.7 and 35.3.
P(27.7<X<35.3)=0.4784

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Jeffrey Jordon
Answered 2021-11-17 Author has 2064 answers

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