Mathematics, 12.02.2021 05:10 NathanMoreno2019

that 45% of adult Americans believe that the overall state of moral values in the United States is poor. (a) Compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans. (b) Interpret the mean. (c) Would it be unusual to identify 240 adult Americans who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans

Answers: 3

Show answers

Answers

Answer from: abhibhambhani

a) The mean is 225 and the standard deviation is 11.12.

b) It means that in samples of 500 adult Americans, the number of those who believe that the overall state of moral values in the United States is poor is expected to be around 225.

c) No, since 240 is less than 2.5 standard deviations from the mean.

Step-by-step explanation:

For each adult American, there are only two possible outcomes. Either they believe the overall state of moral values in the US is poor, or they do not. The adults are independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In the binomial distribution, a value is considered to be unusual if it is more than 2.5 standard deviations from the mean.

45% of adult Americans believe that the overall state of moral values in the United States is poor.

This means that p = 0.45

(a) Compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans.

Sample of 500 means that n = 500

Mean:

E(X) = np = 500*0.45 = 225

Standard deviation:

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.45*0.55} = 11.12$

The mean is 225 and the standard deviation is 11.12.

(b) Interpret the mean.

It means that in samples of 500 adult Americans, the number of those who believe that the overall state of moral values in the United States is poor is expected to be around 225.

(c) Would it be unusual to identify 240 adult Americans who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans

2.5 standard deviations above the mean is:

225 + 2.5*11.12 = 252.8

So 253 or more would be unusual, 240 no.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

i do not know the answer

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Enter the number of complex zeros for the polynomial function f(x) = x 4+ 5x² +6

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

50 people men and women were asked if they watched at least one sport on tv. 20 of the people surveyed are women, but only 9 of them watch at least one sport on tv. 16 of the men watch at least one sport on tv. make a a two-way table and a relative frequency table to represent the data.

Answers: 3

Answer

Mathematics, 21.06.2019 23:30

Abaseball team drinks 10/4 gallons of water during a game. which mixed number represents the gallons of water consumed? a) 1 1/2 gallons b) 2 1/2 gallons c) 2 3/4 gallons d) 3 1/2 gallons

Answers: 2

Answer

Mathematics, 22.06.2019 00:20

How is this equation completed? i cannot find any examples in the book.

Answers: 1

Answer

You know the right answer?

that 45% of adult Americans believe that the overall state of moral values in the United States is p...

Questions