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

Lewis Harvey

Answered question

2021-03-09

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.

Answer & Explanation

Theodore Schwartz

Theodore Schwartz

Skilled2021-03-10Added 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.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-14Added 2605 answers

Answer is given below (on video)

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