MATH 202 Dropbox Assignment #3 Probability

In a recent poll, the Gallup organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 25 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Answer the questions below, showing work. Bare answers are not acceptable. (Showing work may be writing the calculator command you used with correct input values.)

a)Explain why this is a binomial experiment.

a.This is experiment is considered a binomial experiment for a few reasons. The experiment is being performed a fixed number of times which is the same questions that are being asked to the random sample. The trials are also independent. The answers of one participant does not have an affect on any other participant. There is also 2 mutually exclusive outcomes which are either positive or negative feelings about the moral values of the united states.

b)Find and interpret the probability that exactly 15 of those surveyed felt the overall state of moral values in the United States is poor.

a.Using excel, I put in the calculation, "=binom.dist(15,25,.45,false)". After clicking enter I got the answer 0.052023. The probability is this occurring is very low.

c)Find and interpret the probability that no more than 10 of those surveyed felt the overall state of moral

a.Using excel, I put in the calculation, "binom.dist(10,25,.45,true)". After clicking enter I got the answer 0.38426. The probability is below average.

d)Find and interpret the probability that more than 16 of those surveyed felt the overall state of moral values in the United States is poor.

a.Using excel, I put in the calculation, "=1-binom.dist(10,25,.45,true)"

e) Find and interpret the probability that 13 or 14 of those surveyed felt the overall state of moral values in the

United States is poor.

f) Would it be unusual to find 20 or more adult Americans who believe the overall state of moral values in the

United States is poor? Why or why not?

g) Now based on a random sample of 500 adult Americans, compute the mean and standard deviation of the

random variable X, the number of adults who believe the overall state of moral values in the United States is

poor. Interpret the mean.

h) Would it be unusual to identify 240 adult Americans who believe the overall state of moral values in the

United States is poor, based on a random sample of 500 adult Americans? Why?

Now using the Normal Approximation to the Binomial, approximate the probability that:

i) Exactly 250 of those surveyed feel the overall state of moral values in the United States is poor.

j) Between 220 and 250, inclusive, of those surveyed feel the overall state of moral values in the United States is

poor.

k) At least 260 adult Americans who believe the overall state of moral values in the United States is poor,

based on a random sample of 500 adult Americans. Would this be unusual? Why?

Extra credit:

According to www.meretrix.com traffic fatalities occur at a rate of 1.32 fatal accidents per 100 million miles.

Find the probability that, during the next 100 million miles, there will be

a) exactly zero accidents. Interpret the results.

b) at least one fatal accident. . Interpret the results.

C) more than one fatal accident. . Interpret the results.