a. Ecobank Ghana has recently examined the credit card account balances of its customers and found that 20% have an outstanding balance at the credit card limit. Suppose the manager of the credit card division randomly selects 15 customers. Assume that the properties of the binomial distribution apply. i. What is the probability of finding exactly 1 customer in the sample with outstanding balance at the credit card limit? ii. What is the probability that not more than 1 customer in the sample will have balances at the limit of the credit card? iii. What is the probability that exactly 10 of the customers in the sample will have balances below the credit card? ( b. Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes. i. Find the probability that in a given 15-minute segment no customers will arrive at the ATM. Note: e 2.71828. Fol ii. Find the probability that in a given 45-minute segment exactly 8 customers will arrive at the ATM. ( Note: e 2.71828 iii. Find the probability that fewer than 2 customers will arrive in a 30-minute segment.
a. Ecobank Ghana has recently examined the credit card account balances of its customers and found that 20% have an outstanding balance at the credit card limit. Suppose the manager of the credit card division randomly selects 15 customers. Assume that the properties of the binomial distribution apply. i. What is the probability of finding exactly 1 customer in the sample with outstanding balance at the credit card limit? ii. What is the probability that not more than 1 customer in the sample will have balances at the limit of the credit card? iii. What is the probability that exactly 10 of the customers in the sample will have balances below the credit card? ( b. Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to three per 15 minutes. i. Find the probability that in a given 15-minute segment no customers will arrive at the ATM. Note: e 2.71828. Fol ii. Find the probability that in a given 45-minute segment exactly 8 customers will arrive at the ATM. ( Note: e 2.71828 iii. Find the probability that fewer than 2 customers will arrive in a 30-minute segment.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Transcribed Image Text:a. Ecobank Ghana has recently examined the credit card account balances of its customers and
found that 20% have an outstanding balance at the credit card limit. Suppose the manager of
the credit card division randomly selects 15 customers. Assume that the properties of the
binomial distribution apply.
i. What is the probability of finding exactly 1 customer in the sample with outstanding balance at
the credit card limit?
ii. What is the probability that not more than 1 customer in the sample will have balances at the
limit of the credit card?
iii. What is the probability that exactly 10 of the customers in the sample will have balances
below the credit card? (5
b. Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson
distribution with a mean equal to three per 15 minutes.
i. Find the probability that in a given 15-minute segment no customers will arrive at the ATM.
Note: e 2.71828.
tod
ii. Find the probability that in a given 45-minute segment exactly 8 customers will arrive at the
ATM. (
Note: e 2.71828
iii. Find the probability that fewer than 2 customers will arrive in a 30-minute segment.
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