A population of values has a normal distribution with mean =136.4 and standard deviation =30.2. A random sample of size n=158 is drawn. Find the probability that a single randomly selected value is greater than 135. Roung your answer to four decimal places. P(X>135)=?

mattgondek4

mattgondek4

Answered question

2021-01-10

A population of values has a normal distribution with mean =136.4 and standard deviation =30.2. A random sample of size n=158 is drawn.
Find the probability that a single randomly selected value is greater than 135. Roung your answer to four decimal places.
P(X>135)=?

Answer & Explanation

bahaistag

bahaistag

Skilled2021-01-11Added 100 answers

Step 1
The Z-score of a random variable X is defined as follows:
Z=Xμσ
Here, μandσ are the mean and standard deviation of X, respectively.
Step 2
Consider a random variable X, that defines the variable of interest.
According to the given information, X follows normal distribution with mean μx=136.4 and the standard deviation of σx=30.2.
The probability that a single randomly selected value is greater than 135 is,
P(X>135)=1P(Xμσ135136.430.2)
=1P(Z0.046357615)
=10.4815[using the Excel formula=NORM.S.DIST(0.046357615,TRUE)]=0.5185
Therefore, the probability that a single randomly selected value is greater than 135 is 0.5185.

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?