Question

In: Statistics and Probability

Consider a sample with a mean of 65 and a variance of 4. What is the...

Consider a sample with a mean of 65 and a variance of 4. What is the minimum percentage of data within the range 60 to 70. Show work

a. .9043

b. .7672

c. .8400

d. .9401

e. None

Solutions

Expert Solution

Solution:

Given:

Mean = = 65

Variance = s2 = 4

Then standard deviation is square root of variance

thus s = square root of 4

s = 2

We have to find minimum percentage of data within the range 60 to 70.

Use following steps:

and

Thus 60 and 70 are k = 2.5 standard deviations from mean value.

Thus using Chebyshev's theorem, at least % of data fall within k standard deviations from mean.

Thus find:

Thus correct option is: c. 0.8400

orchestra answered 3 years ago
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