A distribution of values is normal with a mean of 203.8 and a standard deviation of 50.2.Find the probability that a randomly selected value is less than 113.4.P(X < 113.4) =?

Lewis Harvey 2021-03-09 Answered

A distribution of values is normal with a mean of 203.8 and a standard deviation of 50.2.
Find the probability that a randomly selected value is less than 113.4.
P(X<113.4)=
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Theodore Schwartz
Answered 2021-03-10 Author has 99 answers

Step 1
Solution:
Let X be the values.
From the given information, X follows normal distribution with mean μ=203.8 and a standard deviation is σ=50.2.
Step 2
Then, the probability that a randomly selected value is less than 113.4 is
P(X<113.4)=P(Xμσ<113.4203.850.2)
=P(Z<1.801)
=0.0359[Using the excel function =NORM.DIST(1.801,0,1,TRUE)]
Thus, the probability that a randomly selected value is less than 113.4 is 0.0359.

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Jeffrey Jordon
Answered 2021-11-14 Author has 2087 answers

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