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

Emily-Jane Bray 2020-12-05 Answered

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 single randomly selected value is between 59.5 and 98.6. P(59.5<X<98.6)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

SoosteethicU
Answered 2020-12-06 Author has 102 answers

From the given information, μ=77, σ=32.2 and the sample size=15.
Consider,
P(59.5<X<98.6)=P(59.5μσ<Xμσ<98.6μσ)
=P(59.57732.2<z<98.67732.2)
=P(0.54348<z<0.6770807)
=P(z<0.6770807)P(z<0.54348)
=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 single randomly selected value is between 59.5 and 98.6 is 0.4554.

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Jeffrey Jordon
Answered 2021-11-14 Author has 2581 answers

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