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

Answer:

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

Step-by-step 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

$Z = \frac{x-mean}{S.D} = \frac{12-10}{1} =2$

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