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The data set has 200observations and has mean 20and standard deviation 4. Approximately how many observations lie between 16and 24.

Short Answer

Expert verified

Zero observations lie between 16and 24.

Step by step solution

01

Given information

We are given that the data has 200observations.

Mean x=20

Standard deviation s=4

We have to find how many observations lies between 16and 24

02

Simplify

According to Chebyshev's Rule for any quantitative data set and any real number kgreater than or equal to 1, at least 1-1k2of the observations lie within kstandard deviations to either side of the mean, that is, between x-ksand x+ks.

Now,

x-ks=1620-k4=16k=1x+ks=2420+k4=24k=1

Therefore, number of observations between 16and 24will be 1-1k2=1-11=0

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