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

Anonym

Answered question

2020-10-28

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.

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2020-10-29Added 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.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-14Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?