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Chapter 3: Q. 3.118 (page 122)

A quantitative data set of size 200has mean 20and standard deviation 4. At least how many observations lie between8and32?

Short Answer

Expert verified

At least178observations lie between8and32.

Step by step solution

01

Given information.

We have been given that,

Mean=20, Standard deviation =4, data set=200

We need find the number of observations lie between8and32.

02

Simplify.

Chebyshev's rule: At least 1001-1k2%of the data values lie within kstandard deviation from the meank>1.

Using Chebyshev's Rule with k=3, we know that at least

1001-1k2%=1001-132%=10089%=89%

is within three standard deviation from the mean.

Determine the value that are three standard deviation from the mean,

20-3脳4=820+3脳4=32

At least 89%of the observations lie between 8and 32.

The number of observation is the product of the percentage and sample size

89%脳200=178

Thus , at least 178observations lie between 8and 32.

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Most popular questions from this chapter

Augusta National Golf Course. Earlier in this section, we found that the population standard deviation of the lengths of the holes at the Augusta National Golf Club is 132.0yd. In this context. is the number 132.0a parameter or a statistic? Explain your answer.

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