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Probability Distributions

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5. A frequency distribution is shown below. Complete parts (a) through (e).
The number of dogs per household in a small town
Dogs 0 1 2 3 4 5
Households 1261 438 169 46 27 11
(a) Use the frequency distribution to construct a probability distribution.
(b) Find the mean of the probability distribution.
(c) Find the variance of the probability distribution.
(d) Find the standard deviation of the probability distribution.
(e) Interpret the results in the context of the real-life situation.

6. Students in a class take quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution.Complete parts (a) through (e).

a) Use the probability distribution to find the mean of the probability distribution.
b) Use the probability distribution to find the variance of the probability distribution.
c) Use the probability distribution to find the standard deviation of the probability distribution.
d) Use the probability distribution to find the expected value of the probability distribution.
e) Interpret the results.

9. About 40% of babies born with a certain ailment recover fully. A hospital is caring for seven babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

a) is the experiment a binomial experiment?

b) What is a success in this experiment?

c) Specify the value of n.

11. 38% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each name his or her favorite nut. Find the probability that the number who say cashews are their favorite nuts is (a) exactly three (b) at least four and (c) at most two.

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The solution contains several statistical problems using the application of probability distribution. The determination of mean, variance and standard deviation of various probability distributions are also discussed.

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