A population of values has a normal distribution with \mu=182.5 and \sigma=49.4. You intend to draw a random sample of size n=15. Find the probability that a single randomly selected value is greater than 169.7. P(X > 169.7) =? Write your answers as numbers accurate to 4 decimal places.

sjeikdom0 2021-02-16 Answered
A population of values has a normal distribution with μ=182.5 and σ=49.4. You intend to draw a random sample of size n=15.
Find the probability that a single randomly selected value is greater than 169.7.
P(X>169.7)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

SkladanH
Answered 2021-02-17 Author has 80 answers

Step 1
Solution:
Let X be the value.
From the given information, X follows normal distribution with mean μ=182.5 and a standard deviation σ=49.4. The sample size is 15.
Step 2
The probability that a single randomly selected value is greater than 169.7 is
P(X>169.7)=P(Xμσ>169.7182.549.4)
=P(Z0.259)
=1P(Z<0.259)
=10.3978=0.6022[Using the excel function=NORM.DIST(0.259,0,1,TRUE)]

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

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