Exam P Practice Problem 107 – wait time at a busy restaurant
Both 107A and 107B use the following probability density function.
Problem 107A
The wait time (in minutes) for a table at a busy restaurant on the weekend is distributed according to the density function given above.
A customer plans to dine in this restaurant on two different weekends.
Determine the expected value of the longest wait of these two visits to the restaurant.
Problem 107B
The wait time (in minutes) for a table at a busy restaurant on the weekend is distributed according to the density function given above.
A customer plans to dine in this restaurant on two different weekends.
Determine the expected value of the shortest wait of these two visits to the restaurant.
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Exam P Practice Problem 106 – average height of students
Problem 106A
Heights of male students in a large university follow a normal distribution with mean 69 inches and standard deviation 2.8 inches.
Four male students from this university are randomly selected.
Determine the probability that the average height of the selected students is between 5 feet 7 inches and 5 feet 11 inches.
Note that one feet = 12 inches.
The answers are based on this normal table from SOA.
Problem 106B
Heights of female students in a large university follow a normal distribution with mean 65 inches and standard deviation 2.2 inches.
Sixteen female students are randomly selected.
Determine the probability that the average height of the selected students is greater than 5 feet 6 inches.
Note that one feet = 12 inches.
The answers are based on this normal table from SOA.
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Exam P Practice Problem 105 – testing electronic devices
Problem 105A
The length of operation (in years) for an electronic device follows an exponential distribution with mean 4. Ten such devices are being observed for one year for a quality control study.
The lengths of operation for these devices are independent.
Determine the probability that no more than three of the devices stop working before the end of the study.
Problem 105B
Twelve patients are randomly selected from a population of patients with history of heart disease to be tracked in a health study. The study begins with an initial assessment of health status. The participants are instructed to return for a follow up visit one year after the initial assessment.
For these patients, the time (in years) from the initial assessment to the next heart attack has an exponential distribution with mean 6.25 years. The times to the next heart attack for these patients are independent.
Determine the probability that ten or more patients experience no heart attack prior to the oneyear follow up visit.
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probability exam P
actuarial exam
math
Daniel Ma
mathematics
dan ma actuarial science
daniel ma actuarial science
Daniel Ma actuarial
2019 – Dan Ma