Question

An insurance company prices its Tornado Insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.02. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the insurance company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 16-year period. Round your answer to four decimal places.

          An insurance company prices its Tornado Insurance using the following assumptions:

• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.02.
• The number of tornadoes in any calendar year is independent of the number
of tornados in any other calendar year.

Using the insurance company's assumptions, calculate the probability that there are
fewer than 2 tornadoes in a 16-year period. Round your answer to four decimal
places.

Show more…

An insurance company prices its Tornado Insurance using the following assumptions:

• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.02.
• The number of tornadoes in any calendar year is independent of the number
of tornados in any other calendar year.

Using the insurance company's assumptions, calculate the probability that there are
fewer than 2 tornadoes in a 16-year period. Round your answer to four decimal
places.

Added by Timothy C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Audrey Fong

06/20/2022

Step 1

This means we are looking for the probability of having either 0 or 1 tornado in this time frame. The number of tornadoes in a year follows a Bernoulli distribution, since a tornado can either occur (with probability 0.02) or not occur (with probability 0.98) in Show more…

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An insurance company prices its Tornado Insurance using the following assumptions: In any calendar year, there can be at most one tornado. In any calendar year, the probability of a tornado is 0.02. The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the insurance company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 16-year period. Round your answer to four decimal places.

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00:01 In this question, when given an insurance company uses the following assumptions to price is tornado insurance.

00:09 In any calendar year, there can be at most one tornado.

00:14 That means, there are two outcomes.

00:18 Either there's a tornado or there isn't a tornado in a year.

00:22 And probability of a tornado in any calendar year is 0 .02.

00:28 Now, the number of tornadoes in any calendar year is independent of the number of tornadoes in any.

00:33 Any other calendar year.

00:35 I'm going to let x be the number of tornadoes in a given 16 year period.

00:41 Now x actually follows the binomial distribution.

00:44 You can see there are four criteria here.

00:47 The number of trials, n is fixed and are identical.

00:51 Now since it's a 16 year period, there will be 16 trials.

00:55 So n is equals to 16.

00:57 In this trial, is to take a look at a year, whether there's a tornado or not.

01:02 So all the 16 trials are identical.

01:05 Hence the first criteria is fulfilled.

01:07 Second criteria each trial is independent.

01:09 While we're given that the number of donados in any year is independent of the other years, so second criteria is fulfilled...

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