According to a survey, 64% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded. When technology is used, use the Tech Help button for further assistance.

Find the probability that exactly 40 of the murders were Cleared.

0.66% probability that exactly 40 of the murders were Cleared.

Step-by-step explanation:

For each murder, there are only two possible outcomes. Either it was cleared, or it was not cleared. The probability of a murder being cleared is independent of other murders. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

64% of murders committed last year were cleared by arrest or exceptional means.

This means that

Fifty murders committed last year are randomly selected.

This means that

Find the probability that exactly 40 of the murders were Cleared.

This is P(X = 40).

0.66% probability that exactly 40 of the murders were Cleared.

b.an increase in a causes b to decrease