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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

User JimmidyJoo
by
8.7k points

2 Answers

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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

User Chris Rice
by
7.5k points
5 votes

Answer-

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

User Matheus
by
9.0k points

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