Question

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data less than 4.2.

A) about 16%

B) about 34%

C) about 50%

D) about 13.5%

Answer 1

It’s A or about 16%,

Answer 2

Answer: A) about 16%

Explanation:

Given: Mean :
`\mu=5.1`

Standard deviation :
`\sigma=0.9`

We know that , the value of z is given by :-

`z=(x-\mu)/(\sigma)`

For x=4.2

`z=(4.2-5.1)/(0.9)=-1`

The p value =
`P(Z<4.2)=P(z<-1)=0.1586553\approx0.16=16\%`

Hence, about 16 % of data is less than 4.2.