Question

A scientist is interested in the effect of time spent with parents and number of hours

youth spend watching television. The researcher knows that the average teen whose
parents work outside the home spends 20 hours a week watching television. The
population mean = 20 and the standard deviation of the distribution is equal to 5.
Calculate the z-scores for the following individual times:________
If X = 5, z= ________
If X = 37, z= ________

Answer 1

Answer: If X = 5, z=-3

If X = 37, z= 3.4

Explanation:

We know that the formula to find the z-score for any random variable x is given by :-

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

, where
`\mu` = Population mean

`\sigma` = Population standard deviation.

As per given , we have

`\mu=20\\\\\sigma=5`

Then , the z-score for x =5

`z=(5-20)/(5)=(-15)/(5)=-3`

i.e. If X = 5, z=-3

When x =37,then
`z=(37-20)/(5)=(17)/(5)=3.4`

i.e. If X = 37, z= 3.4