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Binomial Probability

1. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use a binomial probabilities table to find the probability of x successes given that probability p of successes on a given trial when:

n=2, X=0, and p=.90

2. Three cards selected from a standard 52 card deck without replacement. The number of fives selected recorded. Is this probability a binomial experiment?
Choices:
a. No, because the experiment is not performed at fixed number of times
b. Yes, because the experiment satisfies all criteria of a binomial
c. No, because the trials of the experiment are not independent and probability of success differs from trail to trial
d. No, because there are more than 2 mutually exclusively outcomes for each trial

3. Let the random variable x represent the number of girls in a family with 3 children. Probability of a child being a girl is .48. Construct table describing the probability distribution and find the mean and standard deviation. It is unusual for a family of 3 children to consist of 3 girls?

X= 1, 0, 1, 2, 3
P(X) = ___, _____, ______, _______

Find the mean

Find the standard deviation

Is it unusual for a family of 3 children to consist of 3 girls?

4. Refer to the following data:
Binomial with n=5, and p= 0.146

X= 0,1,2,3,4,5
((X=x)= .4542, .3883, .1328, .0227, .0019, .0001

Probabilities were obtained form entering the values n=5 and p=.146. In a clinical test of a drug, 14.6% of the subjects treated with 10mg of a drug experienced headaches. In each case, assume the subjects are randomly selected and treated with 10mg of the drug. Find the probability that at least 4 of the subjects experienced headaches.

The probability that at least 4 experienced headaches is ______________

5. Assume that procedure yields a binomial distribution with a trial repeated n times, Use a binomial problem of x successes given the probabilities of p successes on a given trial:

n=2, x=0, p=.90

(p(0) =___________

6. A pharmaceutical company receives large shipments of aspirin. The acceptance sampling plan is to randomly select and test 16 tablets, then the whole batch if there is only one of none that doesn't mee the required specifications. If a paricular shipment of thousands of aspirins has a 30% rate of defect, what is the probability that the whole shipment will be accepted.

The probability that his whole shipment will be accepted is______________

7. Assume 12 jurors are selected from a population in which 80% of the people are Mexican-American. The random variables x is the number of Mexican -Americans on the jury:

x p(x)
0 0.000
1 0.000
2 0.000
3 0.000
4 0.001
5 0.003
6 0.016
7 0.053
8 0.133
9 0.236
10 0.283
11 0.206
12 0.069

Find the probability of exactly 8 Mexican-Americans among the 12 jurors
a. P(8)=_____________

b. Find the probability of 8 or fewer Mexican-Americans among the 12 jurors .
The probability of 8 or fewer Mexican-Americans among the 12 jurors is________

Which probability relevant for determining whether 8 jurors among 12 is unusually low: results from a or b?
a. The result from part b because it measures probability of 8 or fewer successes
b. The result from a because it measures the probability of exactly 8 successes

Does 8 Mexican Americans among 12 jurors suggest that the selection process discrimate against Mexican-Americans why or why not?

Yes, because there is greater than a 0.05 probability of it occurring
Yes, because there is less than or equal to a 0.05 probability of occurring
No, because there is less than or equal to o.05 probability of occurring
No, because there is greater than 0.05 probability of occurring

8. In standard English text, a particular letter is used at a rate of 6.9%

a. Find the mean and standard deviation for the number of times this letter will be found on a typical page of 2800 characters.

Mean_______
Standard Deviation_______

b. In an intercepted message, a page of 2800 characters is found to have the letter occur 233 times. Is this unusual?

a. Yes, because 233 is within the range of usual values
b. No, because 233 is within range of usual values
c. Yes, because 233 is below the minimal usual value
d. Yes, because 233 is greater than maximum usual value

9. A candy company claims that 13% of its plain candy are orange, and a sample of 100 such candies is randomly selected.

a. Find the mean and standard deviation of orange candies in such a group of 100.

Mean______
Standard Deviation_______

b. A random sample of 100 candies contain 9 orange candies. Is this unusual? Does it seem that the claim rate of 13% is wrong?

a. No, because 9 is within the range of usual values. Thus, the claim rate of 13% is not necessarily wrong.
b. Yes, because 9 is greater than the maximum usual value. Thus 13% is not necessarily wrong
c. Yes, because 9 is within range of usual claimed value. Thus 13% is probably wrong.
d. Yes, because 9 is below minimum usual value. Thus 13% is not necessarily wrong.

9. There is a .1919 probability that a best of seven game contest will end in 4 games, a 0.2012 will end in 5 games, a 0.2681 will end in 6 games, and a 0.3388 will end in 7 games.

What is the mean probability distribution_____________________

Standard Deviation_____________________

Is it unusual for a team to win in 4 games?

a. Yes, because the probability of a team winning in 4 games is greater than 0.05
b. Yes, " " " is less than or equal to 0.05
c. No, " " "greater than 0.05
d. No, " "" " less than or equal to 0,05.

Solution Summary

The solution provides step by step method for the calculation of binomial probabilities. Formula for the calculation and Interpretations of the results are also included.

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