Question

Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 26% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance. (a) Find the probability distribution of X. [Hint: Let S denote a homeowner that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.26)(0.74)(0.26)(0.26) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) x 0 1 2 3 4 p(x) (b) Draw the corresponding probability histogram. (c) What is the most likely value for X? (d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)

          Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 26% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance.

(a) Find the probability distribution of X. [Hint: Let S denote a homeowner that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.26)(0.74)(0.26)(0.26) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.)

x 0 1 2 3 4
p(x)

(b) Draw the corresponding probability histogram.

(c) What is the most likely value for X?

(d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)

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Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 26% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance.

(a) Find the probability distribution of X. [Hint: Let S denote a homeowner that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.26)(0.74)(0.26)(0.26) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.)

x 0 1 2 3 4
p(x)

(b) Draw the corresponding probability histogram.

(c) What is the most likely value for X?

(d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)

Added by Marc B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert T. L.

10/11/2022

Step 1

74^4 = 0.2999 - P(X=1) = 4 * 0.26 * 0.74^3 = 0.4214 - P(X=2) = 6 * 0.26^2 * 0.74^2 = 0.2221 - P(X=3) = 4 * 0.26^3 * 0.74 = 0.0520 - P(X=4) = 0.26^4 = 0.0046 ** Show more…

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Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 26% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance. (a) Find the probability distribution of X. [Hint: Let S denote a homeowner that has insurance and F denote one who does not. Then one possible outcome is SFSS, with probability (0.26)(0.74)(0.26)(0.26) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) x 0 1 2 3 4 p(x) (b) Draw the corresponding probability histogram. (c) What is the most likely value for X? (d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)

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