# MATHEMATICS

5.5 The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the following results:

Arrivals Frequency

0 14

1 31

2 47

3 41

4 29

5 21

6 10

7 5

8 2

a. Compute the expected number of arrivals per minute.

b. Compute the standard deviation.

5.10 If n=5 and (pie symbol) = .4, what is the probability that

a. X=4?

b. X (smaller than or equal to) 3?

c. X <2?

d. X >1?

5.15 When a customer places an order with Rudy’s OnLine Office Supplies, a computerized accounting information system (AIS) automatically checks to see if the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.05. Suppose that, on a given day, 20 customers place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit is distributed as a binomial random variable.

a. What are the mean and standard deviation of the number

of customers exceeding their credit limits?

b. What is the probability that zero customers will exceed their limits?

c. What is the probability that one customer will exceed his or her limit?

d. What is the probability that two or more customers will exceed their limits?

5.19 Assume a Poisson distribution.

a. If l= 2.0, find P (X (greater than or equal to) 2)

b. If I= 8.0, find P (X (greater than or equal to) 3)

c. If I = 0.5, find P (X (smaller than or equal to) 1)

5.21 Assume that the number of network errors experienced

in a day on a local area network (LAN) is distributed

as a Poisson random variable. The mean number of network

errors experienced in a day is 2.4. What is the probability

that in any given day

a. zero network errors will occur?

b. exactly one network error will occur?

c. two or more network errors will occur?

d. fewer than three network errors will occur?

5.39 Errors in a billing process often lead to customer dissatisfaction and ultimately hurt bottom-line profits. An article in Quality Progress (L. Tatikonda, “A Less Costly Billing Process,” Quality Progress, January 2008, pp. 30–38) discussed a company where 40% of the bills prepared contained errors. If 10 bills are processed, what is the probability that

a. 0 bills will contain errors?

b. exactly 1 bill will contain an error?

c. 2 or more bills will contain errors?

6.1 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that

a. Z is less than 1.57?

b. Z is greater than 1.84?

c. Z is between 1.57 and 1.84?

d. Z is less than 1.57 or greater than 1.84?