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Chapter 2: Q 74. (page 141)

Normal to be foreign-born? The histogram displays the percent of foreign-born residents in each of the 50 states.12 Explain why this distribution of the percent of foreign-born residents in the states is not approximately Normal.

Short Answer

Expert verified

The distribution has been skewed to the right instead of roughly symmetric.

Step by step solution

01

Given information

02

Concept

A dot plot is a graphical display of data using dots.

03

Explanation

The symmetric nature of the Normal distribution is one of its characteristics.

The histogram's distribution is skewed to the right; we can also see that most of the dots in the histogram are to the left, with a tail of less common values to the right.

We know that

The Normal distribution should be symmetric.

And

This distribution has been skewed to the right.

We can say

This distribution is not approximately the Normal distribution.

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Most popular questions from this chapter

Big sharks Here are the lengths (in feet) of 44 great white sharks:

A dot plot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer based on the graph and the 68鈥�95鈥�99.7 rule.

nMeanSDMinQ1MedQ3Max
44155862.559.413.5515.7517.222.8

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Foreign-born residents Refer to Exercise 11 Here are summary statistics for

the percent of foreign-born residents in the 50 states:

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At some fast-food restaurants, customers who want a lid for their drinks get them from a large stack near the straws, napkins, and condiments. The lids are made with a small amount of flexibility so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get very frustrated, especially if they end up spilling their drinks. At one particular restaurant, large drink cups require lids with a 鈥渄iameter鈥� of between 3.95 and 4.05 inches. The restaurant鈥檚 lid supplier claims that the diameter of its large lids follows a Normal distribution with a mean of 3.98 inches and a standard deviation of 0.02 inches. Assume that the supplier鈥檚 claim is true.

Put a lid on it! The supplier is considering two changes to reduce to 1% the percentage of its large-cup lids that are too small. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters.

a. If the standard deviation remains at 蟽=0.02 inch, at what value should the

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b. If the mean diameter stays at 渭=3.98 inches, what value of the standard

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