According to a survey, 62% of murders committed last year were cleared by arrest or exceptional means. Fifty murde 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.

a. Find the probability that exactly 41 of the murders were cleared.
b. Find the probability that between 36 and 38 of the murders, inclusive, were cleared.
c. Would it be unusual if fewer than 19 of the murders were cleared? Why or why not?

a. The probability that exactly 41 of the murders were cleared is . (Round to four decimal places as needed.)

a) The probability that exactly 41 of the murders were cleared is 0.0013

b) The probability that between 36 and 38 of the murders, inclusive, were cleared is 0.0809.

c) Yes, it would be unusual

Step-by-step explanation:

Let p=62% considered as the probability of having a commited that is cleared by arres or exceptional means. We assume that choosing each of the 50 commited is independent of each choose. Then, let X be the number of cleared. In this case, X is distributed as a binomial random variable. Recall that, in this case,

for, with p=0.62

a) We have that

b) We are asked for the following

(The specific calculation is omitted.

c) We will check for the following probability

Given that the probability of this event is really close to 0, it would be unusual if less than 19 murders are cleared.

518,400

step-by-step explanation:

the area is multiplying all the given measurements together.

40 * 18 * 30 * 24 = 518,400

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500