Chapter 13.1, Problem 62STP

a.

To determine

Find the probability that exactly $12$ people are in favor of the new law.

Answer to Problem 62STP

The probability that the people favour will be $0.12$ .

Explanation of Solution

Given: It is given in the question that a polling company wants to estimate the number of people favor of a new environmental law. The polling company polls $20$ people and the probability that a person is in favor of the law is $0.5$ .

Concept Used:

In this, use the concept of probability by using the combination and permutation notations.

Calculation: In this, $\frac{n!}{r!(n-r)!}$ , where $n=20,r=20-12=8$

  $\begin{array}{l}$ \frac{20!}{8!(20-8)!}\times {(0.5)}^1\times 2\times {(0.5)}^8$$ \frac{20!}{8!12!}\times {(0.5)}^1\times {(0.5)}^8$\frac{282172800}{40320}\times 0.001953125\\ 6998.3\times 0.00390625\\ 0.12\\ \end{array}$

The probability will be $0.12$ .

Conclusion:

The probability will be $0.12$ .

b.

To determine

Find the expected number of people favor of the law.

Answer to Problem 62STP

The number of expected people is $10$ .

Explanation of Solution

Given:

It is given in the question that a polling company wants to estimate the number of people favor of a new environmental law. The polling company polls $20$ people and the probability that a person is in favor of the law is $0.5$ .

Concept Used:

In this, use the concept of probability and the formula be total people multiply by its probability of favor.

Calculation:

Here, the total number of people is $20$ .

The probability that a person favor of the law is $0.5$ . Expected people who favor of the law = $20\times 0.5=10$

Conclusion:

The number of expected people is $10$ .