Question

A missing data value from a set of data has a z-score of –2.1. Fred already calculated the mean and standard deviation to be u=43 and o=2 . What was the missing data value? Round the answer to the nearest whole number.

A)39

B)41

C)45

D)47

Answer 1

Answer: A) 39

Explanation:

For any random variable x , the formula to find the z-score is given by :-

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

Given : A missing data value from a set of data has a z-score of –2.1.

Fred already calculated the mean and standard deviation to be
`\mu=43` and
`\sigma=2` .

Substitute all the value in the formula , we get

`-2.1=(x-43)/(2)`

Multiply 2 both sides , we get

`-4.2=x-43`

Add 43 on both the sides , we get

`-4.2+43=x`

Or
`x= 38.8\approx39`

Hence, the missing data value = 39

Answer 2

The missing data value is 39.

Solution-

We know that a Z-score is the number of standard deviations from the mean a data point is. Mathematically it is represented as,

`Z=(X-\mu)/(\sigma )`

Where,

Z = Z-score or standard score,

X = Raw score,

μ = Mean of the sample

σ = Standard deviation

Here, we are given with

Z-score = -2.1

μ = 43

σ = 2

So the raw score or X is missing here, putting the values in teh formula,

`\Rightarrow -2.1=(X-43)/(2)`

`\Rightarrow X-43=-2.1* 2`

`\Rightarrow X=-4.2+43`

`\Rightarrow X=38.8\approx 39`