Question

Home sizes in Anytown, USA have a mean of 2400 square feet and a standard deviation of 450 square feet. What is the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet

Answer 1

0.00084

Explanation:

We are given that

Mean,
`\mu=2400` square feet

Standard deviation,
`\sigma=450`square feet

n=50

We have to find the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet.

`P(x<2200)=P((x-\mu)/((\sigma)/(√(n)))<P((2200-2400)/((450)/(√(50))))`

`P(x<2200)=P(Z<(-200)/((450)/(√(50))))`

Using the formula

`z=(x-\mu)/((\sigma)/(√(n)))`

`P(x<2200)=P(Z<-3.14)`

`P(X<2200)=0.00084`

Hence, the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet=0.00084