A population is normally distributed with mu = 100 and sigma = 25. Find the probability that a value randomly selected from this population will have a value between 95 and 135.

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2022-08-19

A population is normally distributed with μ=100 and σ=25.
Find the probability that a value randomly selected from this population will have a value between 95 and 135.

Answer & Explanation

Terry Avery

Terry Avery

Beginner2022-08-20Added 10 answers

From the provided information,
Population mean (μ ) = 100
Population standard deviation (σ ) = 25
XN(100,25)
The required probability that a value randomly selected from this population will have a value between 95 and 135 can be obtained as:
P(95<X<135)=P(9510025<xμσ<13510025)
=P(-0.2< Z<1.4)
=P(Z<1.4)-P(Z<-0.2)
=0.9192-0.4207 (Using standard normal table)
=0.4985
Thus, the required probability is 0.4985.

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