According to a recent Gallup poll, 20% of Americans believe that healthcare is the most important problem in America. Let p^ be the proportion of people who believe that healthcare is the most important problem in America out of a random sample of 414 Americans. Determine the following probabilities. Round probability solutions to four decimal places, if necessary.

Find the probability that in a random sample of 414 Americans, at least 91 people believe that healthcare is the most important problem in America.

P(p^ > ------) = -----------

Find the probability that in a random sample of 414 Americans, between 58 and 79 people believe that healthcare is the most important problem in America.

p(------ < p^ ------) = -----

2- According to a recent study, more than 900 people move to Florida each day! In fact, data show that only 34% of current Florida residents were born in Florida. Let p^ be the proportion of people who were born in Florida out od a random sample of 251 Florida residents. Determine the following probabilities. Round solutions to four decimal places, if necessary.

P(p^ > 0.32) = ---

Find the probability that a random sample of 251 Florida residents, between 29% and 43% were born in Florida.

P(o.29 < p^ < 0.43) = ---

3- Suppose there exists a population where 31% of its members possess a certain characteristic. Let p^ be the proportion of a random sample of 174 members that also possess that certain characteristic. Determine the following probabilities. Round to four decimal places, if necessary.

Find the probability that the sample proportion is greater than 0.4.

P(p^ > 0.4) = ---

Find the probability that the sample proportion is between 0.24 and 0.3.

P(0.24 < p^ < 0.3) = ---

4- Suppose that 77% of voters in Okeechobee county support a certain candidate for the school board. Consider the sampling distribution of the sample proportion of supporters with sample size n = 173. Determine the mean and standard deviation of the sampling distribution of p^. Round solutions to four decimals, if necessary.

What is the mean of this distribution?

meanp^ =.

What is the standard error of this distribution?

standard errorp^ = -----

5- The average cost to rent a single-family home in Fort Pierce is $1,794 per month. Assume that the distribution of the monthly rent of all single-family homes in Fort Pierce is normally distributed with a standard deviation of $119. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary.

Find the probability that a random sample of 62 homes in Fort Pierce has a mean rent less than $1,750.

P(sampling distribution x < 1750) =----

Find the probability that a random sample of 62 homes in Fort Pierce has a mean rent between $1,760 and $1,840.

P(1760 < sampling distribution x < 1840) =

Some states have college admission programs that guarantee the top p% of high school graduates (in terms of GPA) admission into state university. Suppose a state guarantee the top 13% of high school students admission into its university system. In addition, suppose the distribution of all high school students' GPAs are normally distributed with a mean of 2.97 and standard deviation of 0.15.

Determine the minimum GPA required for a student to be guaranteed admission into the state's university system. Round the solution to two decimal places, if necessary.

GPA =.