EXAM CHAPTER 5, 6, 7
BUSINESS STATISTICS
Number of Cars Proportion
0 0.4
1 0.2
2 0.1
3 0.1
4 0.2
Using the appropriate distribution answer the following questions. Show all your work. Write your answer in the answer box provided.
1. The number of cars in line at Jiffy Lube on E. Washington Ave. during any 30 minute period between the hours of 10am–2pm is given by the distribution on the right.
a. Determine the mean number of cars in line for a 30-minute period.
b. Determine the standard deviation of the number of cars in line during a 30-minute period.
2. According to a recent survey, 55% of all customers who eat at the Olive Garden near East Towne Mall will return at some point and order the same exact meal. Once a person finds something they like they stick to it. Suppose eight customers are selected at random, what is the probability that:
a. exactly five of the customers will order the same meal again?
b. all eight will order the same meal again?
c. at least seven will order the same meal again?
d. at least one will order the same meal again?
e. How many customers would be expected to order the same meal again?
3. The Dane County DNR plants trees at most of the county parks during the fall. Eighty percent of trees planted by the county survive through their first winter. Suppose there were 16 new trees planted at Badger Prairie County Park. What is the probability that:
a. 10 of the 16 trees just planted will survive through the first winter?
b. at least 15 of the trees just planted will survive through the first winter?
4. At the new MATC Market Place, customers order the delicious Panini Sandwiches at an average rate of 24 per hour. What is the probability that exactly 15 people will order a sandwich in the next hour?
5. Dick’s Sporting Goods employs 7 sport specialists and 8 customer service employees. The holidays are right around the corner and they need to gear up for the season. By a random process, management is forming a hiring committee of 4 to handle the upcoming seasonal hiring process. What is the probability that two sport specialists and two customer service employees are selected?
6. American Family Insurance underwrites property & casualty insurance which covers damage from tornados. From historical data the actuaries have estimated that the probability of a tornado touching down in the 250 mile radius around Madison,WI in any one year is 3.5%. If a homeowner takes out a 25-year mortgage on property in Lake Mills, what is the likelihood that the owner will experience at least one tornado touch down during the mortgage period? (hint: use the Poisson distribution, first find the mean --- Probability X is at least 1)
7. A recent study of the individuals who preregistered for the MATC Turkey Trot showed that 40 percent run in other local 5-K runs, 12 percent participate in triathlon’s (which includes biking, swimming and running) and 10 percent do both 5-K runs and triathlon’s. What is the percent of preregistered individuals who sign up for either 5-K runs or triathlons?
8. Halloween is next week. Sun Prairie has always had a great haunted house which draws teenagers from around the county. For the past several years the committee has been collecting data on the time it takes kids to tour through the haunted house. The haunted house tour time is uniformly distributed within a range of 20 minutes to 40 minutes.
a. Determine the height and draw this uniform distribution.
b. How long does the typical haunted house tour take?
c. Determine the standard deviation of the tour time.
d. What is the probability a particular customer will take less than 30 minutes?
e. What is the probability a particular customer will take between 25 and 30 minutes?
9. DISH Network installs digital satellite signal television. Their service department advertises a mean time of 60 minutes for house calls with a standard deviation of 15 minutes. What percentage of house calls are completed: (using the Normal Distribution, be sure to draw the picture):
a. between 60 and 90 minutes?
b. in less than 90 minutes?
c. in less than 60 minutes?
d. Twenty percent of their jobs take more than how much time?
10. Estimate the binomial distribution using the standard normal approximation. Draw the picture.
Lakewood Lumber orders windows from a prominent window manufacturer. The window manufacturer has estimated that 3% of the windows will have locks that lock improperly and are considered defective. Assume a production run of 175 windows is completed.
a. What is the mean and standard deviation of this distribution?
b. What is the probability that 6 or more are defective?
c. What is the probability that exactly 6 windows are defective?
d. What is the probability that there are more than 8 defective file
windows?
11. A sports analyst is hired to provide information on the type of students that will possibly play sports during high school. The data is provided from information on boys & girls in middle school. A random survey is taken of 225 students at local Madison Middle Schools. Of these 225 students, 151 are boys. The students in middle school are grouped by grades, 6th, 7th and 8th. The data is summarized in the table contingency table below:
Boys Girls Total
6th grade 65 16 81
7th grade 50 28 78
8th grade 36 30 66
Totals 151 74 225
A student is selected at random.
a. Find the probability of not selecting a girl.
b. Find the probability of selecting a student in 7th grade.
c. Find the probability of selecting a 7th grade Boy.
d. Find the probability of selecting a 7th grade girl.
e. Find the probability of selecting an 8th grader, given the student selected is a Boy.