Homework Sourse487 of Americans have brown eyes A convention has 5000 peopl
48.7% of Americans have brown eyes. A convention has 5000 people in attendance. Find the mean (expected value),the standard deviation, and the variance for the number of brown-eyed people at such gatherings of 5000 people.
2.
Assume a procedure yields a binomial distribution with a trial repeated 2 times. Using Table A-1, find the probability of 1 or 2 successes given that the probability of success on a single trial is 99%.
Select one:
a. .100
b. .002
c. 1.000
d. .020
3.
Forty percent of Clinton County residents are uncomfortable using the Internet. Suppose 7 such people are randomly selected. What is the probability exactly 5 are uncomfortable using the Internet?
Select one:
a. .025
b. .077
c. .070
d. .194
4.
Given the following probability distribution, calculate the mean, variance, and standard deviation.
x
P(x)
1
0.125
2
0.236
3
0.543
4
0.096
Assume a procedure yields a binomial distribution with a trial repeated 8 times. Using Table A-1, find the probability of 5 successes given that the probability of success on a single trial is 70%
Select one:
a. .136
b. .254
c. .625
d. .296
In a local archery contest, the probability that Samuel will be successful on each shot is 82.5% If Samuel attempts four shots, what is the probability he will be successful on all four shots?
Select one:
a. .410
b. .144
c. .463
d. .393
A basketball player with a history of making 80% of the foul shots taken during games. (Answer all parts for full credit)
What is the probability that he will make exactly 5 of 7 foul shots?
What is the probability that he will make at least 5 of 7 foul shots?
What is the probability that he will MISS at least one of 7 foul shots?
A recent survey shows that 60% of families regularly schedule family vacations for the month of April. Find the probability that at least 5 out of 8 randomly selected families regularly schedule family vacations for the month of April.
Select one:
a. .595
b. .279
c. .164
d. .209
Assume a procedure yields a binomial distribution with a trial repeated 6 times. Using Table A-1, find the probability of 0 successes given that the probability of success on a single trial is 20%
Select one:
a. .118
b. .198
c. .393
d. .262
35% of American households subscribe to TIVO. Suppose that 12 American households are randomly chosen. (Answer both parts for full credit.)
a) How many of them would you expect to have TIVO?
b) What is the probability that 2 OR 3 of them have TIVO?
| x | P(x) |
| 1 | 0.125 |
| 2 | 0.236 |
| 3 | 0.543 |
| 4 | 0.096 |
Solution
48.7% of Americans have brown eyes. A convention has 5000 people in attendance. Find the mean (expected value),the standard deviation, and the variance for the number of brown-eyed people at such gatherings of 5000 people.
n=5000, p=0.487
Expectation = np = 2435
Variance = np(1 - p) = 1249.155
Standard deviation = 35.34338
2. Assume a procedure yields a binomial distribution with a trial repeated 2 times. Using Table A-1, find the probability of 1 or 2 successes given that the probability of success on a single trial is 99%.
n=2, p=0.99
Select one:
a. .100
b. .002
c. 1.000
d. .020
3.Forty percent of Clinton County residents are uncomfortable using the Internet. Suppose 7 such people are randomly selected. What is the probability exactly 5 are uncomfortable using the Internet?
n=7, p=0.4
Select one:
a. .025
b. .077
c. .070
d. .194
4.Given the following probability distribution, calculate the mean, variance, and standard deviation.
x
P(x)
1
0.125
2
0.236
3
0.543
4
0.096
X
P(X)
x*p(x)
(x-mean)^2*p(x)
1
0.125
0.125
0.324013
2
0.236
0.472
0.087816
3
0.543
1.629
0.08259
4
0.096
0.384
0.185482
Total
1.000
2.61
0.6799
Mean =2.61
Variance=0.6799
Sd= sqrt(0.6799) =0.82456
Assume a procedure yields a binomial distribution with a trial repeated 8 times. Using Table A-1, find the probability of 5 successes given that the probability of success on a single trial is 70%
n=8, p=0.70
Select one:
a. .136
b. .254
c. .625
d. .296
In a local archery contest, the probability that Samuel will be successful on each shot is 82.5% If Samuel attempts four shots, what is the probability he will be successful on all four shots?
n=4, p=0.825
Select one:
a. .410
b. .144
c. .463
d. .393
A basketball player with a history of making 80% of the foul shots taken during games. (Answer all parts for full credit)
n=7, p=0.8
What is the probability that he will make exactly 5 of 7 foul shots?
P=0.2753
What is the probability that he will make at least 5 of 7 foul shots?
P=0.852
What is the probability that he will MISS at least one of 7 foul shots?
P=0.7903
A recent survey shows that 60% of families regularly schedule family vacations for the month of April. Find the probability that at least 5 out of 8 randomly selected families regularly schedule family vacations for the month of April.
n=8, p=0.6
Select one:
a. .595
b. .279
c. .164
d. .209
Assume a procedure yields a binomial distribution with a trial repeated 6 times. Using Table A-1, find the probability of 0 successes given that the probability of success on a single trial is 20%
n=6, p=0.2
Select one:
a. .118
b. .198
c. .393
d. .262
35% of American households subscribe to TIVO. Suppose that 12 American households are randomly chosen. (Answer both parts for full credit.)
n=12, p=0.35
Expectation = np = 4.2
b) What is the probability that 2 OR 3 of them have TIVO?
P = P(x=2)+P(x=3) =0.1098+0.1954=0.3042
| x | P(x) |
| 1 | 0.125 |
| 2 | 0.236 |
| 3 | 0.543 |
| 4 | 0.096 |
