Probability 4 Some More Probability Distributions
1. Which of the following is not a property of a binomial trial?
a)
there are two possible outcomes to each trial
b)
the outcome of each trial is independent
c)
the probability of ‘success’ is always greater than 0.5
d)
the probability of failure plus the probability of success equals one
2. In the context of Binomial distributions, what is a ‘combination’?
a)
the number of ways of selecting x objects from n objects
b)
the probability of selecting a specific object
c)
the number of ways that x selected objects can be arranged
d)
the number of ways of combining probabilities of events
3. What is the value of 10C4?
a)
10
b)
40
c)
210
d)
5040
4. In how many ways can 5 people form pairs to play a game of badminton doubles?
a)
5
b)
20
c)
10
d)
12
5. What is the equation for a Binomial probability?
a)
P(x) = μe-μx
b)
P(x) = nCx px(1-p)n-x
c)
P(x) = μxe-μ/x!
d)
P(x) = 2σ2 e –(x – μ)/2σ
6. If a coin is tossed 5 times, what is the probability of getting two heads?
a)
0.0312
b)
0.0624
c)
0.3125
d)
0.9688
7. If a coin is tossed 5 times, what is the probability of getting at least 2 heads?
a)
0.1875
b)
0.8125
c)
0.3125
d)
0.4
8. If the probability of success in a Binomial trial is 0.1, what is the probability of more
than 2 successes in ten trials?
a)
0.1
b)
0.0702
c)
0.01
d)
0.00
9. If a Binomial trial has a probability of success p, what is the mean number of
successes in n trials and the variation?
a)
p and p2
b)
p and np
c)
np and np2
d)
np and np(1-p)
10. Which of the following is not required to approximate a Binomial distribution by a
Normal distribution?
a)
The probability of success is small
b)
The number of trials is large
c)
np ≥ 5
d)
n(1-n) ≥ 5
11. A random variable, X, comes from a binomial distribution with n = 60 and p = 0.2.
Calculate (approximately) P(X ≤ 20)?
a)
0.8413
b)
0.5842
c)
0.9969
d)
0.3333
12. Which of the following random variables have a Poisson probability distribution?
a)
The number of drivers stopping at a roadside flower stand within an hour
b)
The weight of a packet of crisps produced by a particular process
c)
The number of the winning greyhound at a particular race track
d)
The amount of rainfall recorded at a particular weather station
13. The shape of a Poisson distribution depends on the constant e and which variable?
a)
the probability of success
b)
the probability of failure
c)
the standard deviation
d)
the mean number of occurrences
14. What is the equation for a Poisson probability?
a)
P(x) = μe-μx
b)
P(x) = nCx px(1-p)n-x
c)
P(x) = μxe-μ/x!
d)
P(x) = 2σ2 e –(x – μ)/2σ
15. The average number of accidents at a particular road junction in a year is 2.5 and
assumed to follow a Poisson distribution. What is the probability there are no road
accidents at the junction in a given year?
a)
0
b)
1
c)
0.205
d)
0.082
16. If an average of five people an hour arrive at an office, what is the probability of
exactly five arriving in an hour?
a)
0.1755
b)
0.2
c)
0.3510
d)
0.5
17. If an average of five people an hour arrive at an office, what is the probability that at
least three people arrive in an hour?
a)
0.5
b)
0.6
c)
0.6489
d)
0.8754
18. If an event occurs randomly an average of nine times an hour, what are the mean and
variance of the number of occurrences?
a)
3 and 3
b)
9 and 9
c)
9 and 4.583
d)
27 and 4.583
19. What is the equation for an exponential distribution?
a)
P(x) = μe-μx
b)
P(x) = nCx px(1-p)n-x
c)
P(x) = μxe-μ/x!
d)
P(x) = 2σ2 e –(x – μ)/2σ
20. When do the time intervals between events follows an exponential distribution?
a)
always
b)
when the number of events in a time interval follows a Binomial distribution
c)
when the number of events in a time interval follows a Poisson distribution
d)
never
21. The visitors arrive randomly at an office at a mean rate of 0.4 a minute. How is the
time between successive visitors distributed?
a)
a Poisson distribution with mean 0.4
b)
an exponential distribution with mean 0.4
c)
an exponential distribution with mean 2.5
d)
we cannot say without more information
22. The visitors arrive randomly at an office at a mean rate of 0.4 a minute. The time
between successive visitors has an exponential distribution with mean 2.5.What is the
mean time between visitor arrivals, and the variance?
a)
b)
c)
d)
0.4 and 0.4
0.4 and 2.5
2.5 and 2.5
2.5 and 0.4167
23. If events occur at an average of 5 an hour, what is probability of waiting less than 12
minutes between calls?
a)
0.6321
b)
0.5
c)
0.3679
d)
0.8187
24. The time (in minutes) between phone calls at a computing help desk is known to have
an exponential distribution with mean 2 minutes. What is the probability that there is
less than one minute between calls?
a)
0.3935
b)
0.632
c)
0.5
d)
0.6065
Question Answer
1
C
2
A
3
C
4
C
5
B
6
C
7
B
8
B
9
D
10
A
11
C
12
A
13
D
14
C
15
D
16
A
17
D
18
B
19
A
20
C
21
C
22
D
23
A
24
A