A population of values has a normal distribution with \mu=99.6 and \sigma=35.1. You intend to draw a random

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Answered question

2021-01-05

A population of values has a normal distribution with μ=99.6 and σ=35.1. You intend to draw a random sample of size n=84.
Find the probability that a sample of size n=84 is randomly selected with a mean between 98.5 and 100.7.
P(98.5<X<100.7)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2021-01-06Added 110 answers

Step 1
From the provided information,
Mean (μ)=99.6
Standard deviation (σ)=35.1
XN(99.6,35.1)
Sample size (n)=84
Step 2
The required probability that a sample of size n=84 is randomly selected with a mean between 98.5 and 100.7 can be obtained as:
and 100.7 can be obtained as:
P(98.5<X<100.7)=P(98.599.635.184<xμσn<100.799.635.184)
=P(0.287<Z<0.287)
=P(Z<0.287)P(Z<0.287)
=P(Z<0.287)[1P(z<0.287)]
=2P(Z<0.287)1
=2(0.6129)1=0.2258 (Using standard normal table)
Thus, the required probability is 0.2258.

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