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Chapter 3: Q. 3.123 (page 123)

The data set has mean 30and standard deviation4 . Approximately what percentage of the observations lie between 22and 38?

Short Answer

Expert verified

The percentage of the observations lie between 22and 38 is95%.

Step by step solution

01

Given information

We are given that data set has mean 30and standard deviation4 .

02

Explanation

We will use empirical rule, to determine approximate values for the percentage of observations between 22and 38.

We are given that μ=30andσ=4 , where is mean and is standard deviation.

Also , the given interval 22,38will be formed by adding and subtracting standard deviations from the mean. We will check for different values of .

So using the value of mean and standard deviation , we get ,μ-kσ,μ+kσ=(22,38)⇒k=2

By empirical rule , Pμ-2σ<X<μ+2σ≈0.95where is given interval.

So percentage is95%

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Most popular questions from this chapter

Explain in detail the purpose of a measure of center.

Consider the data set: 1,2,3,4,5,6,7,8,9.

a) Obtain the mean and median of the data.

b) Replace the 9in the data set by 99and again compare the mean and median. Decide which measure of the center works better here and explain your answer.

c) For the data set in part b) the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result.

The data set has 80observations and has mean 30and standard deviation 5. Approximately how many observations lie between20 and40 ?

We have provided simple data set for you to practices the basics of finding measures of center. For each data set determine the:

a) Mean

b)Median

c) Mode.

The given data set is3,5,7

Copperhead and Tiger Snakes. S. Fearn et al. compare two types of snakes in the article “Body Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania” (Australian Journal of Zoology, Vol. 60, No. 3, pp. 159-165). Tiger snakes and lowland copperheads are both large snakes confined to the cooler parts of Tasmania. The weights of the male lowland copperhead in Tasmania have a mean of 812.07 g and a standard deviation of 330.24 g; the weights of the male tiger snake in Tasmania have a mean of 743.65 g and a standard deviation of 336.36 g.
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c. Assuming that a comparison using z-scores is legitimate, relative to the other snakes of its type, which snake is heavier?
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