Question 1: Score 0/0
The probability of getting a parking ticket when not paying for a 2-hour period is 0.25.
What is the probability of getting at least 75 tickets if you park on 257 occasions for a
2-hour period and don’t pay?
Let X be the number of tickets received.
This is a binomial situation wp = 0.25 and n = 257 ,
soMean = np = 64.25 ,
Using a Normal approximation with Continuity Correction we have
Thus, P(X ≥ 75) ≈ 1 - P(Z < 1.476579) = 0.0699.
Question 2: Score 0/0
Assume that the tires sold by Olsen Tires are normally distributed
with a mean life of 41,000 miles and a standard deviation of 2,450
miles. If you were to buy 4 Olsen tires, what is the approximate
probability that all four will last longer than 40,000 miles?
t: Let X = tire lifetime. E(X) = 41,000 anX σ = 2,450. We standardize X by setting .
Now consider a single tire, and let's find the probability that its lifetime is 40,000 miles or more. That is
The probability that all four tires will last this long, assuming their lifespans are independent, is (0.6584) =
Question 3: Score 0/0
If X is a normal random variable with mean 5 and standard deviation 2.9, then find the
value x such that
P(Z > x) is equal to 0.7263, as shown below. (Note: the diagram is not necessarily to Incorrect
scale.) Your Answer:
Correct Answer: 3.2551
Comment: P(X > x) = 0.7263 means 1 - P(X < x) = 0.7263 so P(X < x) = 1 - 0.7263 = 0.2737
Standardizing: so using the Inverse Normal we have :
Question 4: Score 0/0
If a baseball player's batting average is 0.314 or 31.4%, find the probability that the
player will have a bad season and only score at most 67 hits in 235 times at bat. (4
NOTE: Please answer with a probability, not a %. For example 0.1234 instead of
12.34 . Incorrect
Let X be the number of hits in 235 at-bats. We use the normal approximation to the binomial here.
Question 5: Score 0/0
Suppose at the University of Manitoba, 34.3% of the students live in apartments. If 178 students
are randomly selected, then the probability that the number of them living in apartments will be
between 49 and 68 inclusive, is (4 decimals):
Correct 0.8564±0.001 Answer:
Comment Let X be the number of students in apartments.
This is a binomial distribution p = 0.343 and n = 178 .
Mean = np = 61.054, Var = np(1 - p) = 40.1125 , soSD = 6.3334
Using the normal approximation we continuity correction we have:
Question 6: Score 0/0
Defects occur in a certain manufactured tape on the average of 1 per 1,000
m. Assuming a Poisson distribution for the number of defects in a given
length of tape, what is the probability that a 4,000 m roll will have no
defects? (3 decimal accuracy) Incorrect
Correct Answer: 0.0183±0.01
Let X = number of defects in a 4,000 m roll. X ~ Poisson(4). P(X = 0) = = 0.0183 .
Question 7: Score 0/0
A series of n independent trials are run for a Binomial Process with probability of success p. If
the mean is found to be 2.9 and the variance is 1.4, what would you estimate n to be?
Correct Answer: 6
Comment: We have μ = 2.9 and σ = 1.4 . Using the properties of the Binomial Distribution we have :
 np = 2.9 and
 np(1-p) = 1.4
Combining : 2.9(1-p) = 1.4 so or = 0.517241
Substitute this p value in  and solve::
For n you really should round UP to the next integer, but "normal" roundoff is accepted.
Question 8: Score 0/0 The World Series terminates when one team wins its fourth game.
Suppose the two teams are evenly matched, so each has probability
1/2 of winning any one game. What is the probability that the series
will take 5 games?
We have a binomial situation. Define success as team A winning a game. Then p = = 1 - p and n
= 5 . The correct calculation (for the answer ) is shown in red below:
P(Series terminates at the end of 4 games) = P(A wins all 4 or B wins all 4)
Consider the case where B wins all 4. Then x = 0 and:
P(series ends in 4 with B the winner) = P(X = 0; n = 4, p = 0.5) =
By symmetry, P(series ends in 4 with A the winner) = , so
P(series ends in 4) =
P(Series terminates at the end of 5 games) = 2P(A wins in 5) by the symmetry of A and B
= 2 P(A wins exactly 3 of the first 4, then fifth)
= 2 P(X = 3; n = 4, p = )P(A wins 5th)
P(Series ends after 6th game)= P(A wins in 6 OR B wins in 6)= 2P(A wins in 6) by the symmetry of A
= 2P(A wins 3 of the first 5)P(A wins 6th)
= 2 P(X = 3; n = 5, p = )
= 2 P(Series runs 7 games)= P(even after 6 games)
= P(X = 3; n = 6, p = )
Question 9: Score 0/0