Math 227 Collection Homework #2 Name: 1. The following data represent the length

Question

Math 227 Collection Homework #2 Name: 1. The following data represent the lengths in inches of 27 fish that were caught in a lake 7, 8, 8, 8,9,9, 10, 11, 11, 11, 12, 13, 14, 14, 15,17, 17, 17,18, 20, 20, 21, 24, 27, 28, 31,47 a. Find the 5-number summary for the data, and determine whether there are any outliers using the interquartile range criterion. b. Create a boxplot for the data, accounting for any outliers. Police catch the perpetrator in a burglary 60% of the time. Suppose that 5 such crimes are committed in a week. Find the following probabilities: a. All five are caught. b. Less than two are caught. c. Exactly 3 are caught. Suppose that lightning strikes a tower once every 10 years on average Find the following probabilities: a. Lightning strikes the tower three times in 10 years. b. Lightning never strikes the tower in 20 years. c. Lightning strikes the tower at least twice in 10 years.

Explanation / Answer

Solution:-

2)

p = 0.60, n = 5

a) The probability that all five are caught is 0.07776.

x = 5

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 5) = 0.07776

b) The probability that less than two are caught is 0.08704.

x = 2

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 2) = 0.08704

c) The probability that exactly three are caught is 0.3456

x = 3

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 3) = 0.3456.

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