Question

Suppose that a recent poll found that 40% of adults in a certain country believe that the overall state of moral values is poor. If a survey of a random sample of 55 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral? values, complete parts? (a) through? (d) below. Use the Tech Help button for further assistance.?

(a) Find the probability that exactly21 of those surveyed feel the state of morals is poor. The probability that exactly 21 of those surveyed feel the state of morals is poor is nothing.?(Round to four decimal places as? needed.)?
(b) Find the probability that no more than22of those surveyed feel that state of morals is poor. The probability that no more than 22 of those surveyed feel that state of morals is poor is nothing.?(Round to four decimal places as? needed.)?
(c) Find the probability that more than22 of those surveyed feel the state of morals is poor. The probability that more than22 of those surveyed feel the state of morals is poor is nothing.?(Round to four decimal places as? needed.)?
(d) Find the probability that15 or 16 believe the state of morals is poor. The probability that 15 or 16 believe the state of morals is poor is nothing.?(Round to four decimal places as? needed.)

Answer 1

Explanation:

Let X be the no of adults whose feelings the state of morals is poor.

X has two outcomes and each trial is independent of the other

X is Bin with p = probability for success in each trial =40%=0.40

n=no of adults surveyed = 55

a) The probability that exactly 21 of those surveyed feel the state of morals is poor is

`P(X=21) = 40C21 (0.4)^(21) (1-0.4)^(19) \\=0.03519`

(b) The probability that no more than 22 of those surveyed feel that state of morals is poor is

=
`P(X<22)\\=0.9811`

(c) The probability that more than22 of those surveyed feel the state of morals is poor is

`P(X>22)\\=1-0.9811\\=0.0119`

(d) The probability that 15 or 16 believe the state of morals is poor is

=
`P(X=15)+P(X=16)\\=0.1228+0.1279\\=0.2507`