STA237 (Probability, Statistics and Data Analysis I) - Fall 2022
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STA237 (Probability, Statistics and Data Analysis I) - Fall 2022
Selvakkadunko Selvaratnam
Assignment 1
Q1. A total of 108 students filled out a survey for a psychology class project. A total of
36 students indicated they were athletes. Of those students, 21 said they preferred to work out in the morning as opposed to the afternoon. For the nonathletes, 25 said they preferred to work out in the morning. Find the following probabilities for a randomly selected student who took the survey:
(a) P (Athlete given prefer morning workout).
(b) P (Prefer morning workout given nonathlete).
(c) P (Nonathlete given prefer nonmorning workout).
Q2. A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate
the costs of 30%, 20%, and 50%, respectively, of all jobs bid on by the company. For i = 1, 2, 3, define Ei to be the event that a job is estimated by engineer i. The following probabilities describe the rates at which the engineers make serious errors in estimating costs: P (error|E1 ) = .01, P (error|E2 ) = .03, and P (error|E3 ) = .02
(a) If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 1?
(b) If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 2?
(c) If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 3?
(d) Based on the probabilities given in parts (a)– (c), which engineer is most likely responsible for making the serious error?
Q3. An insurance policy costs $500 and will pay policyholders $50000 if they suffer a major
injury (resulting in hospitalization) or $10000 if they suffer a minor injury (resulting in lost time from work). The company estimates that each year, 1 in every 5000 policyholders may have a major injury, and 1 in 1250 may have a minor injury.
(a) Create a probability model for the profit on a policy.
(b) What is the company’s expected profit on this policy?
(c) What is the standard deviation of the profit on this policy?
Q4. A wildlife biologist examines frogs for a genetic trait he suspects may be linked to
sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in one of every 10 frogs. He collects and examines 15 frogs. If the frequency of the trait has not changed, what is the probability that he finds the trait in
(a) none of the 15 frogs?
(b) at least two frogs?
(c) three or four frogs?
(d) no more than five frogs?
Q5. The number of ways you can choose r things from a set of n, ignoring the order in
which they are chosen, is / 、r(n) = 
. Let x be the first element of the set of n
things. We can partition the collection of possible size r subsets into those that contain
x and those that don’t: there must be 
、 subsets of the first type and /n r(-) 1、
subsets of the second type. Thus
/ 、r(n) = 
、+ /n r(-) 1、.
Using this and the fact that / 、n(n) = / 、0(n) = 1, write a recursive function to calculate / 、r(n) .
Q6. Customers arrive at a checkout counter in a department store according to a Pois-
son distribution at an average of eight per hour. During a given hour, what are the probabilities that
(a) no more than five customers arrive?
(b) at least three customers arrive?
(c) exactly ten customers arrive?
(d) between three and seven, which includes three and seven, customers arrive?
2022-10-06