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Chapter 2: Q R2.9. (page 148)

Assessing Normality Catherine and Ana gave an online reflex test to33 varsity

athletes at their school. The following Normal probability plot displays the data on reaction times (in milliseconds) for these students. Is the distribution of reaction times for these athletes approximately Normal? Why or why not?

Short Answer

Expert verified

Not approximately normal.

Step by step solution

01

Given information

The figure is:

02

Explanation

Around a reaction time of 200ms, there is a considerable curvature in the normal probability lot, indicating that the pattern in the Normal probability plot is not substantially linear. This suggests, however, that the distribution is not approximately normal. Because the pattern is concave up on the left side of the normal probability plot, the distribution seems to be slightly skewed to the right.

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Most popular questions from this chapter

Used cars, cheap! A used-car salesman has 28 cars in his inventory, with prices ranging from \(11,500 to \)25,000. For a Labor Day sale, he reduces the price of each car by $500. What effect will this reduction have on each of the following characteristics of the resulting distribution of price?

a. Shape

b. Mean and median

c. Standard deviation and interquartile range (IQR)

Mean and median The figure displays two density curves that model different

distributions of quantitative data. Identify the location of the mean and median by letter for each graph. Justify your answers.

Household incomes The cumulative relative frequency graph describes the distribution of median household incomes in the 50 states in a recent year.

a. The median household income in North Dakota that year was $55,766Is North Dakota an unusually wealthy state?

b. Estimate and interpret the 90th percentile of the distribution.

Deciles The deciles of any distribution are the values at the 10th,20th,…,and 90th percentiles. The first and last deciles are the 10th and the 90th percentiles, respectively. What are the first and last deciles of the standard Normal distribution?

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 “diameter” of between 3.95 and 4.05 inches. The restaurant’s 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’s 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 σ=0.02 inch, at what value should the

supplier set the mean diameter of its large-cup lids so that only 1% is too small to fit?

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

deviation will result in only 1% of lids that are too small to fit?

c. Which of the two options in parts (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)σ=0.02
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