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Gwar [14]
3 years ago
12

An article in American Demographics claims that more than twice as many shoppers are out shopping on the weekends that during th

e week. Not only that, such shoppers also spend more money on their purchases on Saturdays and Sundays! Suppose that the amount of money spent at shopping centers between 4 P.M. and 6 P.M. on Sundays has a normal distribution with mean $85 and with a standard deviation of $20. A shopper is randomly selected on a Sunday between 4 P.M. and 6 P.M. and asked about his spending patterns.
a. What is the probability that he has spent more than $95 at the mall?
b. What is the probability that he has spent between $95 and $115 at the mall?
c. If two shoppers are randomly selected, what is the probability that both shoppers have spent more than $115 at the mall?
Mathematics
1 answer:
Monica [59]3 years ago
7 0

Answer:

0.3085,0.2417,0.0045

Step-by-step explanation:

Given that X, the amount of money spent at shopping centers between 4 P.M. and 6 P.M. on Sundays has a normal distribution with mean $85 and with a standard deviation of $20.

X is N(85, 20)

To convert into std normal variate we use the following formula

Z=\frac{x-85}{20}

a) the probability that he has spent more than $95 at the mall

=P(X>95) = P(Z>0.5)=\\0.5-0.1915\\=0.3085

b.  the probability that he has spent between $95 and $115 at the mall

=P(95

c. If two shoppers are randomly selected, what is the probability that both shoppers have spent more than $115 at the mall

=product of two probabilities since independent

= {P(X>115)}^2\\= P(Z>1.5)*P(Z>1,5)\\= 0.0668^2\\=0.0045

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