Probability Calculations in Statistics
The time required to complete a certain construction project
follows a normal distribution with a mean of 43 weeks and a standard deviation
of 3.7 weeks. Use this information to answer questions 1 through 3.
1. What is the probability of the completing the project in
no more than 48 weeks?
2. What is the probability of the completing the project in more
than 37.9 weeks?
3. What is the probability of completing the project between
36 weeks and 49 weeks?
The students in a certain college course recently completed
an exam. 14 students earned an A, 11 students earned a B, 10 students earned a
C, 11 students earned a D and 11 students earned an F on the exam. The students
were queried regarding the number of hours they had devoted to studying for the
exam. 12 of the students who earned an A, 9 of the students who earned a B, 7
of the students who earned a C, 3 of the students who earned a D, and 1 of the
students who earned an F reported that they had devoted more than 8 hours to
studying for the exam. The remaining students reported that they had devoted no
more than 8 hours to studying for the exam. Use this information to answer
questions 4 through 6.
4. What is the probability of a randomly selected student
having devoted no more than 8 hours to studying for the exam?
5. What is the probability of a randomly selected student
having earned a C, D or F on the exam?
6. What is the probability of a randomly selected student
having earned a C, D or F on the exam given they devoted more than 8 hours to
studying for the exam?
Your professor tells you that if you earn a score of 90% or
better on your midterm exam, then there is an 80% chance you will earn an A for
the course. You estimate that you have only a 55% chance of earning a score of
90% or better on the midterm exam. Use this information to answer question 7.
7. What is the probability that your score on the midterm
exam will be 90% or better and you will receive an A for the course?
A sample consisting of freshman college students was
surveyed regarding the average number of hours of television they expected to
watch daily during the current semester. The student responses are summarized
in the table below. Assume that the sample was representative of all freshman
students. Use this information to answer question 8.
Number of Hours. Number of Students
5 or more. 53
4 41
3. 37
2. 25
1. 10
0 1
8. What is the probability that a randomly selected freshman
student will watch two or fewer hours of television daily during the current
semester?
A student has an important exam coming up and is
contemplating not studying for the exam in order to attend a concert with his
friends. The student knows the exam will consist of twenty-five multiple choice
questions with four possible answers for each question. The student also knows that
he must earn a minimum score of 76% on the exam in order to successfully
achieve his desired grade for the course. Use this information to answer
questions 9 and 10 based upon modeling this situation as a binomial experiment.
9. What is the probability that the student will
successfully earn exactly the required minimum score of 76% on the exam based
solely upon randomly guessing the answer for each question?
10. What is the probability that the student will earn less
than the required minimum score of 76% on the exam based solely upon randomly
guessing the answer for each question?
A standard deck of playing cards consists of fifty-two
cards. The cards in each deck consist of four suits, namely spades (?), clubs
(?), diamonds (?) and hearts (?). Each suit consists of thirteen cards, namely
ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2. Use this information to
answer question 11.
11. What is the probability of selecting four cards of the
same suit in four consecutive draws from a randomly shuffled deck of playing
cards, assuming the specific cards that must be selected are not important, the
order in which the cards must be selected is not important, and the suit is not
important?
Customers arrive at a supermarket check-out counter
following a Poisson distribution with an average arrival rate of 5 customers
per hour. Use this information to answer questions 12 through 14.
12. What is the probability of less than 5 customers
arriving at the supermarket check-out counter in a given one hour period?
13. What is the probability of exactly 5 customers arriving
at the supermarket check-out counter in a given one hour period?
14. What is the probability of more than 5 customers
arriving at the supermarket check-out counter in a given one hour period?
A local commuter bus service advertises that its buses run
every 15 minutes along a certain route. Assume that the bus service follows an
exponential distribution. Use this information to answer questions 15 through
17.
15. What is the probability of a bus picking up the
passengers at a given bus stop in no more than 15 minutes?
16. What is the probability of a bus picking up the
passengers at a given bus stop in more than 15 minutes?
17. What is the probability of a bus picking up the
passengers at a given bus stop in between 15 and 25 minutes?
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