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Used cars, cheap! Refer to Exercise 24Suppose each car鈥檚 price is reduced by 10% instead of $500What effect will this discount have on each of the following characteristics of the resulting price distribution?

a. Shape

b. Median

c. Interquartile range (IQR)

Short Answer

Expert verified

Part (a) Shape will remain unaffected.

Part (b) Median is reduced by 10%

Part (c) Interquartile range decreases by 10%

Step by step solution

01

Part (a) Step 1: Given information

Each car鈥檚 price is reduced by 10% instead of a $500

Every car鈥檚 price gets reduced by 10%

02

Part (a) Step 2: Explanation

90Instead of the prior price of 100percent, the new price is 90 percent (or 0.90). As a result, each price must be multiplied by 0.90When every value in the data is multiplied by 0.90, the structure of the distribution remains unchanged since the associations between each data pair remain unchanged. As a result, the new price's distribution shape is identical to the previous price's distribution shape.

03

Part (b) Step 1: Explanation

As a result, the new price is 90 percent (or 0.90) lower than the prior price of 100 percent. As a result, each price must be multiplied by 0.90 The Median is a measure of the center, as we all know. When every value in the data is multiplied by 0.90 the distribution's center is multiplied by 0.90 as well. As a result, the Median is also multiplied by 0.90 We can also state that the median has been reduced by 10%

04

Part (c) Step 1: Explanation

0.90As a result, the new price is 90percent (or 0.90) lower than the prior price of 100percent. As a result, each price must be multiplied by 0.90The interquartile range is a measure of variability, as we all know. When every value in the data is multiplied by 0.90 the distribution's variability is multiplied by 0.90as well. As a result, the interquartile range is multiplied by 0.90

We can also argue that the interquartile range (IQR) has shrunk by 10%

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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.

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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?

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