Download Exam #1 - Solution 27/10/2009

Exam #1 - Solution
27/10/2009
Question #1:
The probability that a particular type of smoke alarm will function properly and sound an alarm in the
presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.
1. Find the probability that both sound an alarm in the presence of smoke.
ANSWER:
0.64
2. Find the probability that neither sound an alarm in the presence of smoke
ANSWER:
0.04
3. Find the probability that at least one sounds an alarm in the presence of smoke.
ANSWER:
0.96
4. Find the probability that at most one sounds an alarm in the presence of smoke.
ANSWER:
0.36
5. Find the mean and the standard deviation of sound an alarm in the presence of smoke.
ANSWER:
1.6, 0.566
Question #2:
1. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6
outages per year. Find the probability that there will be exactly 3 power outages in a year.
ANSWER:
0.0892
2. Find the probability that there will be at least 3 power outages in a year.
ANSWER:
0.9380
3. Find the probability that there will be no more than 1 power outage in a year.
ANSWER:
0.0174
4. Find the mean and the variance of the number of power outages.
ANSWER:
6
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Question #3:
If we know that the length of time it takes a college student to find a parking spot in the library parking
lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute.
1. Find the probability that a randomly selected college student will find a parking spot in the library
parking lot in less than 3 minutes.
a) 0.3551
b) 0.3085
c) 0.2674
d) 0.1915
ANSWER:
b
2. Find the probability that a randomly selected college student will take between 2 and 4.5 minutes to
find a parking spot in the library parking lot.
a) 0.0919
b) 0.2255
c) 0.4938
d) 0.7745
ANSWER:
d
3. Find the point in the distribution in which 75.8% of the college students exceed when trying to find a
parking spot in the library parking lot.
a) 2.8 minutes
b) 3.2 minutes
c) 3.4 minutes
d) 4.2 minutes
ANSWER:
a
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In
addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a
score greater than 90 is 6.68%.
1. What is the probability of a score greater than 95?
ANSWER:
2.27% or 0.0227
2. What is the probability of a score between 75 and 90?
ANSWER:
43.32% or 0.4332
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