A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size n = 153 is drawn. Find the probability that a sample of size n=153 is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places. P=?

EunoR 2021-03-01 Answered
A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size n=153 is drawn.
Find the probability that a sample of size n=153 is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places.
P=?
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Adnaan Franks
Answered 2021-03-02 Author has 92 answers
The probability that a sample size n=153 is randomly selected with a mean between 188 and 206.6 is obtained below:
From the given information, a population of values has a normal distribution with mean 191.4 and standard deviation of 69.7 and sample of size n=153.
here,
if X(μ,σ) then X(μ,σn)
The required value is given below:
P(188X206.6)=P(X206.6)P(X188)
=P(Z206.6191.469.7153)P(Z188191.469.7153)
=P(Z15.25.635)P(Z3.45.635)
=P(Z2.70)P(Z0.60)
=0.99650.2743=0.7222
Thus, the probability that a sample size n=153 is randomly selected with a mean between 188 and 206.6 is 0.7222.
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Jeffrey Jordon
Answered 2021-11-14 Author has 2047 answers
Jeffrey Jordon
Answered 2021-11-14 Author has 2047 answers

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