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U.S. consumers are increasingly viewing debit cards as a convenient substitute f

ID: 3336946 • Letter: U

Question

U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,750 (Kiplinger’s, August 2007). Assume that the average amount spent on a debit card is normally distributed with a standard deviation of $500. Use Table 1. a. A consumer advocate comments that the majority of consumers spend over $9,000 on a debit card.

Find a flaw in this statement. (Round "z-value" to 2 decimal places and final answer to 4 decimal places.)

The proportion of consumers who spend over $9,000

b. Compute the 25th percentile of the amount spent on a debit card. (Round "z-value" to 2 decimal places.) 25th percentile

c. Compute the 75th percentile of the amount spent on a debit card. (Round "z-value" to 2 decimal places.) 75th percentile

d. What is the interquartile range of this distribution? (Round "z-value" to 2 decimal places.) Interquartile range

Explanation / Answer

a) Flaw:

95% of people lie between 2 SD

So, 7750 + 2 * 500 = 8750

It cant happen that majority lie above 9000

b) z for 25th percentile (use normal table) = - 0.67

(x - 7750)/500 = -0.68

x = 7410

c) z for 75th percentile (use normal table) = 0.67

(x - 7750)/500 = 0.67

x = 8090

d) IQR = 8090 - 7410 = 680