COMM215 CH 5 CONCORDIA UVERSITY TEST WITH ACCURATE
SOLUTIONS
1. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X > 4).
.0102
.0870
.0778
.3370
P(X = 5) = (.4) = .0102
5
2. Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over
the last 100 weeks show 6 weeks with no radios sold, 27 weeks with one radio sold, 35 weeks with
two radios sold, 20 weeks with three radios sold, 9 weeks with four radios sold, and 3 weeks with
five radios sold. Calculate μx, σx2, and σx, of x, the number of ClearTone-400 radios sold at Sound
City during a week using the estimated probability distribution. (Round your answers to 2 decimal
places.)
µx 2.08
1.33
σx 1.15
(a)
μx = 0 × 0.06 + 1 × 0.27 + 2 × 0.35 + 3 × 0.20 + 4 × 0.09 + 5 × 0.03 = 2.08
(b)
σx2 = (0-2.08)2 × 0.06 + (1-2.08)2 × 0.27 + (2-2.08)2 × 0.27 + (3-2.08)2 × 0.35 + (4-2.08)2 × 0.20 + (5-
2.08)2 × 0.09
= 0.2596 + 0.3149 + 0.0022 + 0.1693 + 0.3318 + 0.2558 = 1.33
(c)
σx = SQRT(1.33) = 1.15
3. If x is a binomial random variable, then the standard deviation of x is given by
npq.
np.
√npq.
(npq)2.
4. Which one of the following statements is not an assumption of the binomial distribution?
Trials are independent of each other.
Each trial results in one of two mutually exclusive outcomes.
Sampling is with replacement.
The experiment consists of n identical trials.
The probability of success remains constant from trial to trial.
5. In the most recent election, 19 percent of all eligible college students voted. If a random sample of 20
students were surveyed, find the probability that none of the students voted.
.0148
.0014
.4997
, .0000
P(X) = n!/[x!(n − x)!] × p (1 − p) , for x = 0 when p = .19 and n = 20.
x n−x
6. A total of 50 raffle tickets are sold for a contest to win a car. If you purchase one ticket, what are your odds
against winning?
.05
.01
50 to 1
49 to 1
Probability of losing = 1 − probability of winning = 1 − 1/50 = 49/50.
7. The binomial distribution is characterized by situations that are analogous to
coin tossing.
measuring the length of an item.
drawing balls from an urn.
counting defects on an item.
Binomial distributions assume a constant probability of success.
8. The number of ways to arrange x successes among n trials is equal to
n!(n−x)n!(n−x).
n!x!n!x!.
nxnx.
n!/x!(n−x)!.
9. When p = .5, the binomial distribution will be symmetric.
sometimes
always
never
10. Which of the following is a valid probability value for a discrete random variable?
.2
All of the choices are correct.
1.01
−.7
The probability of a discrete random variable can only be between 0 and +1.
11. According to data from the state blood program, 40 percent of all individuals have group A blood. If six
individuals give blood, find the probability that none of the individuals has group A blood.
.0041
.0467
.4000
.0410
P(x = 0) = .0467
SOLUTIONS
1. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X > 4).
.0102
.0870
.0778
.3370
P(X = 5) = (.4) = .0102
5
2. Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over
the last 100 weeks show 6 weeks with no radios sold, 27 weeks with one radio sold, 35 weeks with
two radios sold, 20 weeks with three radios sold, 9 weeks with four radios sold, and 3 weeks with
five radios sold. Calculate μx, σx2, and σx, of x, the number of ClearTone-400 radios sold at Sound
City during a week using the estimated probability distribution. (Round your answers to 2 decimal
places.)
µx 2.08
1.33
σx 1.15
(a)
μx = 0 × 0.06 + 1 × 0.27 + 2 × 0.35 + 3 × 0.20 + 4 × 0.09 + 5 × 0.03 = 2.08
(b)
σx2 = (0-2.08)2 × 0.06 + (1-2.08)2 × 0.27 + (2-2.08)2 × 0.27 + (3-2.08)2 × 0.35 + (4-2.08)2 × 0.20 + (5-
2.08)2 × 0.09
= 0.2596 + 0.3149 + 0.0022 + 0.1693 + 0.3318 + 0.2558 = 1.33
(c)
σx = SQRT(1.33) = 1.15
3. If x is a binomial random variable, then the standard deviation of x is given by
npq.
np.
√npq.
(npq)2.
4. Which one of the following statements is not an assumption of the binomial distribution?
Trials are independent of each other.
Each trial results in one of two mutually exclusive outcomes.
Sampling is with replacement.
The experiment consists of n identical trials.
The probability of success remains constant from trial to trial.
5. In the most recent election, 19 percent of all eligible college students voted. If a random sample of 20
students were surveyed, find the probability that none of the students voted.
.0148
.0014
.4997
, .0000
P(X) = n!/[x!(n − x)!] × p (1 − p) , for x = 0 when p = .19 and n = 20.
x n−x
6. A total of 50 raffle tickets are sold for a contest to win a car. If you purchase one ticket, what are your odds
against winning?
.05
.01
50 to 1
49 to 1
Probability of losing = 1 − probability of winning = 1 − 1/50 = 49/50.
7. The binomial distribution is characterized by situations that are analogous to
coin tossing.
measuring the length of an item.
drawing balls from an urn.
counting defects on an item.
Binomial distributions assume a constant probability of success.
8. The number of ways to arrange x successes among n trials is equal to
n!(n−x)n!(n−x).
n!x!n!x!.
nxnx.
n!/x!(n−x)!.
9. When p = .5, the binomial distribution will be symmetric.
sometimes
always
never
10. Which of the following is a valid probability value for a discrete random variable?
.2
All of the choices are correct.
1.01
−.7
The probability of a discrete random variable can only be between 0 and +1.
11. According to data from the state blood program, 40 percent of all individuals have group A blood. If six
individuals give blood, find the probability that none of the individuals has group A blood.
.0041
.0467
.4000
.0410
P(x = 0) = .0467
