Question

If a data point has a corresponding z-score of -1.5, then it is one and a half standard deviations above the mean value. 1. True 2. False

Answer 1

Answer: False.

Explanation:

For any random variable x,

Formula to calculate the z-score :
`z=(x-\mu)/(\sigma)`

, where
`\mu` = Mean

`\sigma` = Standard deviation

Let x be the data point has a corresponding z-score of -1.5.

Then , we have

`-1.5=(x-\mu)/(\sigma)`

`-1.5\sigma=x-\mu`

`\mu-1.5\sigma=x`

i.e. x is one and a half standard deviations below the mean value.

( one and a half =
`1+(1)/(2)=1.5` )

Therefore , the given statement is false.