A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.Find the probability that a randomly selected value is between 151.4 and 283.7.P(151.4 < X < 283.7) = IncorrectWrite your answers as numbers accurate to 4 decimal places.

Anonym 2020-10-28 Answered

A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.
Find the probability that a randomly selected value is between 151.4 and 283.7.
P(151.4<X<283.7)= Incorrect
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

2k1enyvp
Answered 2020-10-29 Author has 94 answers

Step 1
Solution:
Let X be the value.
From the given information, X follows normal distribution with a mean μ=166.1 and a standard deviation is σ=73.5.
Step 2
Then, the probability that a randomly selected value is between 151.4 and 283.7 is
P(151.4<X<283.7)=P(151.4166.173.5<Xμσ<283.7166.173.5)
=P(0.200<Z<1.600)
=P(Z<1.600)P(Z<0.200)
=0.94520.4207[Using the excel function=NORM.DIST(1.600,0,1,TRUE)=NORM.DIST(0.200,0,1,TRUE)]=0.5245
Thus, the probability that a randomly selected value is between 151.4 and 283.7 is 0.5245.

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Jeffrey Jordon
Answered 2021-11-14 Author has 2070 answers

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