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Chapter 3: Q. 3.128 (page 123)

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

Short Answer

Expert verified

The observations that lie between20and40 are approximately76

Step by step solution

01

Given information

We are given that data set has80 observations and has mean 30and standard deviation5.

02

Explanation

We will use empirical rule, to determine approximate values for the of observations between 20and 40.

We are given that μ=30andσ=5, where is mean and is standard deviation.

Also , the given interval 20,40will 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=(20,40)⇒k=2

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

So percentage is 95%

To find observations, we will use95%of80=76

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Most popular questions from this chapter

Simple data sets have been given for you to try locating the descriptive metrics mentioned in this section. For each data set separately.

(a) Calculate the quartiles,

(b) calculate the interquartile range

(c)compile a five-number summary.

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Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.

Identify a use of lower and upper limits.

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