A population of values has a normal distribution with \mu=77 and \sigma=32.2.

avissidep

avissidep

Answered question

2020-12-22

A population of values has a normal distribution with μ=77 and σ=32.2. You intend to draw a random sample of size n=15
Find the probability that a sample of size n=15 is randomly selected with a mean between 59.5 and 98.6. P(59.5<X<98.6)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

faldduE

faldduE

Skilled2020-12-23Added 109 answers

From the given information, μ=77, σ=32.2 and the sample size=15.
Consider,
P(59.5<X<98.6)=P(59.5μ(σn)<Xμ(σn)<98.6μ(σn))
=P(59.5μ(32.215)<z<98.677(32.215))
=P(2.10488<z<2.59803)
=P(z<2.59803)P(z<2.10488)
=0.7488280.2934=0.4554[From the Excel function=NORM.DIST(0.6770807,0,1,TRUE)=NORM.DIST(0.54348,0,1,TRUE)]
Thus, the probability that a sample of size n=15 is randomly selected with a mean between 59.5 and 98.6 is 0.9777.

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