Question

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors have prices that were less than $3.12 per gallon

Answer 1

`P(x<3.12)= 0.21186`

Explanation:

Mean
`\=x=\$3.20`

Standard deviation
`\sigma =\$0.10`

Estimated price
`y=\$3.12`

Generally the equation for P(x<3.12) is mathematically given by

`P(x<3.12)=P((y-x)/(\sigma)<-(3.12-3.20)/(0.10))`

`P(x<3.12)=(z<-0.8)`

Since from Z table

`P(x<3.12)= 0.21186`

Therefore the proportion of the milk vendors that have prices that were less than $3.12 per gallon is

`P(x<3.12)= 0.21186`