Worksheet 5 (Chapter 3): Probability II
Name: ______________________________________________
Section: _________________________
For any of the following questions be sure to show appropriate work and give appropriate probability statements. 1. Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.
Intended
Enrollment
Status
Full-Time
Part-Time
Totals
Undergraduate Major
Business
Engineering
352
197
150
161
502
358
Other
251
194
445
Totals
800
505
1305
a. If a student intends to attend classes full-time in pursuit of an MBA degree, what is
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What is the probability that he will make at least one shot?
Sample Space (makes both, makes first misses second, misses first makes second, misses both)
P(makes at least one out of two) = 1 – P(misses both) = 1 – (0.07)(0.07) = 0.9951
c. What is the probability that he will miss both shots?
P(misses both) = (0.07)(0.07) = 0.0049
3. Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (Associated Press, January 16, 2006). The results of the study of consumers older than 18 provided the following probabilities.
• The probability that a consumer uses a plastic card when making a purchase is 0.37.
• Given that the consumer uses a plastic card, there is a 0.19 probability that the consumer is 18 to
24 years old.
• Given that the consumer uses a plastic card, there is a 0.81 probability that the consumer is more than 24 years old.
US Census Bureau data show that 14% of the consumer population is 18 to 24 years old.
a. Given the consumer is 18 to 24 years old, what is the probability that the consumer uses a plastic card? Uses plastic
Does not use plastic
18 – 24
(0.37)(.19) = 0.0703
0.14 – 0.0703 = 0.0697
0.14
Older than 24
(0.37)(0.81) = 0.2997
0.86 – 0.2997 = 0.5603
1.00 – 0.14 = 0.86
Total
0.37
1.00 – 0.37 = 0.63
1.00
P(plastic | 18 to 24) = 0.0703/0.14 = 0.5021
b. Given the consumer is over 24 years old, what is the probability that the
4. Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary)
28. The Polo Development Firm is building a shopping center. It has informed renters that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping center is completed is estimated to be 14 months, with a standard deviation of 4 months, what is the probability that the renters will not be able to occupy in 19 months?
Life insurance company …. With a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75?
8. The measure of how likely an event will occur is probability. Match the following probability with one of the statements. There is only one answer per statement.
d. The normal distribution may be a useful approximation, but it can’t exactly be the correct distribution. Explain why this is so.
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Explain why we need to use the t distribution. What assumption do you need to make?
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