Question

3 these sample e. Note that one person in the sample played 32 What effect, if any, does this large value have on each of the three measures of location? Discuss. f. For these sample data, which measure of location provides the best measure of the center of the data? Discuss. g. Given this sample data, suppose the manager wishes to give discounts to golfers in the top quartile. What should the minimum number of rounds played be to receive a discount? 3-83. The Zagat Survey®, a leading provider of leisure-based survey results, released its New York City report that showed an average price per meal of $48.56 (source: www.zagat.com). a. If the standard deviation of the price of meals in New York City was $10, determine the largest proportion of meal prices that could be higher than $60. b. If the checks were paid in Chinese currency ($1 USD = 6.46 Chinese yuan), determine the mean and standard deviation of meal prices in New York City. How would this change of currency affect your answer to part a? Computer Software Exercises 3-84. The AJ Fitness Club is a full-service fitness center that offers its members the latest in weight machines, cardio equipment, and exercise classes. The company has surveyed its members to learn how satisfied they are with the services provided by the club. The data for this survey are in the file called AJFitness. a. Calculate the mean and median age for those

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Answer 1

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Let the variable X denote the price per meal in New York City

We assume that the survey is done on large data therefore, X follows normal distribution.

$mean: \mu =48.56$

$: \sigma =10$

- Z
  $;Z\sim N(0,1)$

a.  $P(X>60)=1-P(X\leq 60)$

$=1-P(\frac{X-\mu }{\sigma }\leq \frac{60-48.56}{10})$

$=1-P(Z\leq 1.144)$

$\simeq 1-P(Z\leq 1.14)$

$=1-\Phi ( 1.14)=1-0.87285=0.12515\simeq 0.13$

Therefore, the largest proportion of meal prices that could be higher than $60 = 0.13

b. $1USD = 6.46 Chinese yuan

If the checks were paid in Chinese currency

Mean $=48.56\times 6.46=313.6976$

Standard deviation $=10\times 6.46=64.6$

$60 $=60\times 6.46=387.6$ Chinese yuan

$P(X>387.6)=1-P(X\leq 387.6)$

$=1-P(\frac{X-\mu }{\sigma }\leq \frac{387.6-313.6976}{64.6})$

$=1-P(Z\leq 1.144)$

$\simeq 1-P(Z\leq 1.14)$

$=1-\Phi ( 1.14)=1-0.87285=0.12515\simeq 0.13$

Therefore, the largest proportion of meal prices that could be higher than 387.6 Chinese yuan = 0.13

Since, the proportion remain unchanged therefore, the change of currency does not affect our answer in part a.