A population of values has a normal distribution with \mu = 216.9 and \sigma = 87.1. You intend to draw a random sample of size n = 97.Find the probability that a single randomly selected value is between 193 and 244.3.P(193<X<244.3) =?Write your answers as numbers accurate to 4 decimal places.

waigaK 2021-02-19 Answered

A population of values has a normal distribution with μ=216.9 and σ=87.1. You intend to draw a random sample of size n=97.
Find the probability that a single randomly selected value is between 193 and 244.3.
P(193<X<244.3)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Theodore Schwartz
Answered 2021-02-20 Author has 99 answers

Step 1
From the provided information,
Mean (μ)=216.9
Population standard deviation (σ)=87.1
Sample size (n)=97
XN(216.9,87.1)
Step 2
The required probability that a single randomly selected value is between 193 and 244.3 can be obtained as:
P(193<X<244.3)=P(193216.987.1<xμσ<244.3216.987.1)
=P(0.274<Z<0.315)
=P(Z<0.315)P(Z<0.274)
=0.62360.3920=0.2316 (Using standard normal table)
Thus, the required probability is 0.2316.

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Jeffrey Jordon
Answered 2021-11-17 Author has 2027 answers

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