Just before a referendum on a school​ budget, a local newspaper polls 357 voters to predict whether the budget will pass. Suppose the budget has the support of 53​ percent of the voters. What is the probability that the​ newspaper's sample will lead it to predict​ defeat?

When Donald Trump was campaigning for President , 65% of constituents supported his policy on legalizing marijuana. Today, Donald Trump is wondering if the support for legalizing marijuana has changed. If he polls 100 constituents, what is the probability of finding more than 58% still support the policy?

A group of students consisting of 20 males and 20 females were selected to participate in a research study.  If the students were selected using random sampling, what is the probability of picking a female student?

A news station polls 405 voters to predict whether a budget will pass. Suppose the budget has support form 55% of voters. What is the probability the news station's smaple will lead to predict defeat?

In Franklin County, there are about 50,000 registered voters, of whom 15,000 are Democrats. A survey organization is about to take a simple random sample of 1,000 registered voters. There is about a 50-50 chance that the percentage of Democrats in the sample will be bigger than ?

Jenny works for a local brewing company. She and her team mates try to estimate the Hong Kong consumers’ preference on their beer brand compared to other imported ones. They performed a survey asking if the respondent prefers the company’s brand the most or not. Based on this survey result, they want to decide how much money the company needs to invest on brand promotions in the coming year. This is an important decision for the company, and the management wants to have the probability that the sample proportion p is +/- 3% from the actual proportion p to be very high (i.e., at least 99%). In this case, what is the desirable sample size n for the following two cases? Give the answer in the form of: at least ___ x100 samples. Case i. When the actual proportion is 50%. Case ii. When the actual proportion is 10%. Explain why the sample sizes required to achieve the same accuracy in the two cases are different.

A national sports equipment co-op is going to conduct a survey of its members. It knows from collecting data when members join that 68% of them identify as male. Assuming the total number of members is very large and 200 of them are randomly selected to take the survey, what’s the chance less than 60% of these randomly chosen members identify as male? Show all your work and write your answer as a percentage.

The Mighty Mouse Amusement park fills to capacity 73.1% of the time. Out of 3 randomly selected days, what is the probability that the park has at least one day filled to capacity. Round to four 4 decimals.

Suppose a basketball player makes 57.7% of shots and that the probabilty of making each shot is independent. If the basketball player attempts 3 shots, what is the probability of making at least one shot? Enter your answer rounded to at least 4 decimals.

There are 6 radar stations and the probability of a single radar station detecting an enemy plane is 0.65. Identify the type of histogram for the probability distribution.