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
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