A population of values has a normal distribution with μ=13.7 and σ=22. You intend to...

Tahmid Knox

Tahmid Knox

Answered

2020-12-06

A population of values has a normal distribution with μ=13.7 and σ=22.
You intend to draw a random sample of size n=78.
Find the probability that a single randomly selected value is less than 11.5.
P(X<11.5)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

Szeteib

Szeteib

Expert

2020-12-07Added 102 answers

Step 1
From the provided information,
Mean (μ)=13.7
Standard deviation (σ)=22
Let X be a random variable which represents the score.
XN(13.7,22)
Sample size (n)=78
Step 2
The required probability that a single randomly selected value is less than 11.5
can be obtained as:
P(X,11.5)=P(xμσ<11.513.722)
=P(Z<0.1)=0.4602 (Using standard normal table)
Thus, the required probability is 0.4602.

Jeffrey Jordon

Jeffrey Jordon

Expert

2021-11-17Added 2575 answers

Answer is given below (on video)

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