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Chapter 3: Q. 3.129 (page 123)

The data set has 250observations and has mean 100and standard deviation 16. Approximately how many observations lie between 52and 148.

Short Answer

Expert verified

222observations lie between 52and148.

Step by step solution

01

Given information

We are given that the data has 250and

Mean x=100

Standard deviation s=16.

We have to find number of observations between 52and 148.

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=52100-k16=52k=3x+ks=148100+k16=148k=3

Therefore, number of observations between 52and 148are

1-1k2=1-132=0.8890.889脳250鈮�222

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