Question

A normal distribution has a mean of 10 and a standard deviation of 1. What is the probability of selecting a number that is at least 12?

Leave the answer in decimal form to 3 decimal places.

Answer 1

The probability of selecting a number that is at least 12 = 0.0228

Explanation:

Explanation:-

Given mean of the normal distribution 'μ '= 10

Standard deviation of the normal distribution 'σ' = 1

Let 'X' be the random variable of Normal distribution

Let X = 12

`Z = (x-mean)/(S.D) = (12-10)/(1) =2`

The probability of selecting a number that is at least 12

P( X > 12 ) = P( Z >2 )

= 1- P( Z < 2)

= 1 - ( 0.5 +A(2))

= 1 - 0.5 -A(2)

= 0.5 - A(2)

= 0.5 - 0.4772

= 0.0228

The probability of selecting a number that is at least 12 = 0.0228