The number of dogs per household in a small town

Dogs	0	1	2	3	4	5
Probability	0.660	0.210	0.087	0.025	0.013	0.006

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Part 1

(a) Find the mean, variance, and standard deviation of the probability distribution.

Find the mean of the probability distribution.

mu =

(Round to one decimal place as needed.)

Part 2

Find the variance of the probability distribution.

sigma squared =

(Round to one decimal place as needed.)

Part 3

Find the standard deviation of the probability distribution.

sigma =

(Round to one decimal place as needed.)

Part 4

(b) Interpret the results in the context of the real-life situation.

A.

A household on average has 0.5 dog with a standard deviation of 11 dogs.

B.

A household on average has 0.5 dog with a standard deviation of 0.9 dog.

C.

A household on average has 0.9 dog with a standard deviation of 0.5 dog.

D.

A household on average has 0.8 dog with a standard deviation of 0.9 dog.

2. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A newspaper finds that the mean number of typographical errors per page is

three

.

Find the probability that (a) exactly four typographical errors are found on a page, (b) at most four typographical errors are found on a page, and (c) more than four typographical errors are found on a page.

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Part 1

(a) P(exactly four typographical errors are found on a page)=

(Round to four decimal places as needed.)

Part 2

(b) P(at most four typographical errors are found on a page)=

(Round to four decimal places as needed.)

Part 3

(c) P(more than four typographical errors are found on a page)=

(Round to four decimal places as needed.)

Part 4

Which of the events are unusual? Select all that apply.

A.

The event in part (a) is unusual.

B.

The event in part (b) is unusual.

C.

The event in part (c) is unusual.

D.

None of the events are unusual.

3. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A football player completes a pass

64.2 % of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes.

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Part 1

(a) P(the first pass he completes is the second pass)=

(Round to three decimal places as needed.)

Part 2

(b) P(the first pass he completes is the first or second pass)=

(Round to three decimal places as needed.)

Part 3

(c) P(he does not complete his first twopasses)=

(Round to three decimal places as needed.)

Part 4

Which of the events are unusual? Select all that apply.

A.

The event in part (a), P(the first pass he completes is the second pass), is unusual.

B.

The event in part (b), P(the first pass he completes is the first or second pass), is unusual.

C.

The event in part (c), P(he does not complete his first two passes), is unusual.

D.

None of the events are unusual.

4. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the last century, the mean number of major hurricanes to strike a certain country's mainland per year was about

0.59. Find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.

Question content area bottom

Part 1

(a) P(exactly one major hurricane will strike the mainland)=

(Round to three decimal places as needed.)

Part 2

(b) P(at most one major hurricane will strike the mainland)=

(Round to three decimal places as needed.)

Part 3

(c) P(more than one major hurricane will strike the mainland)=

(Round to three decimal places as needed.)

Part 4

Which of the events are unusual? Select all that apply.

A.

The event in part (a) is unusual.

B.

The event in part (b) is unusual.

C.

The event in part (c) is unusual.

D.

None of the events are unusual.