Quiz 4

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Refer to Exhibit 5-7. The expected number of cups of coffee is:

1.20

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The probability that there are less than 3 occurrences is:

A .1016

The following table provides a probability distribution for the random variable x. x f(x) 3 .25 6 .50 9 .25 A. Compute E(x), the expected value of x. B.Compute 2, the variance of x (to 1 decimal). C. Compute , the standard deviation of x (to 2 decimals).

A. 6 B. 4.5 C. 2.12

If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the:

Poisson probability distribution

onsider a binomial experiment with n = 20 and p = .70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. Compute P(x 16) (to 4 decimals). d. Compute P(x 15) (to 4 decimals). e. Compute E(x). f. Compute Var(x) (to 1 decimal) and (to 2 decimals).

a. f(12) = C(20,12)*(0.7)^12*(0.3)^8=0.1144 b. f(16) = C(20,16)*(0.7)^16*(0.3)^4=0.1304 c. .2375 d. .7625 e. E(x) = np = 20(0.7) = 14 f. Var(x) = npq = 20*0.7*0.3=4.2 s = sqrt(4.2) = 2.05

The binomial probability distribution is used with:

a. a discrete random variable.

A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

b. .0038

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

b. .0142

The standard deviation of a binomial distribution is:

b. None of these alternative answers are correct.

The following represents the probability distribution for the daily demand of microcomputers at a local store. Refer to Exhibit 5-1. The probability of having a demand for at least two microcomputers is:

.7

The probability distribution for the daily sales at Michael's Co. is given below. Refer to Exhibit 5-2. The probability of having sales of at least $50,000 is:

.90

The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). a.What is the expected value of the job satisfaction score for senior executives (to 2 decimals)? b. What is the expected value of the job satisfaction score for middle managers (to 2 decimals)? c. Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals). Executives Middle managers d. Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives Middle managers e. What comparison can you make about the job satisfaction of senior executives and middle managers?

E(Senior)= (1*.05)+(2*.09)+(3*.03)+(4*.42)+(5*.41)=4.05 E(Middle)= (1*.04)+(2*.10)+(3*.12)+(4*.46)+(5*.28)=3.84 Var(Senior)= (17.65)-(4.05^2)=1.2475 Var(middle)= (15.88)-(3.84^2)=1.1344 Std(Senior)= sqrt(1.2475)= 1.1169 Std(Middle)= sqrt(1.1344)= 1.0552 For Question E the answer is "Senior Executives have a higher satisfaction with more variation."

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution. x 0 1 2 3 The mean and the standard deviation for the number of electrical outages (respectively) are:

b. .26 and .577

A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. If required, round your answers to two decimal places. Develop a probability distribution for the duration of a service call. Duration of Call x f(x) 1 2 3 4 Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below. Does this probability distribution satisfy equation (5.1)? Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?

google it lol

The probability distribution for the daily sales at Michael's Co. is given below. Refer to Exhibit 5-2. The expected daily sales are:

d. $56,000