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Chapter 3: Q. 3.131 (page 123)

The data set has 150observations and has mean 35and standard deviation 4. Approximately how many observations lie between 31and 39?

Short Answer

Expert verified

Zero observations lies between 31and 39.

Step by step solution

01

Given information

We are given that the data has 150observations and

Mean x=35

Standard deviation s=4

We have to find number of observations between 31and 39

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, according to given data

x-ks=3135-k4=31k=1x+ks=3935+k4=39k=1

Therefore, number of observations between 31and 39 are 1-1k2=1-1=0

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