Just before a referendum on a school budget, a local newspaper polls 412 voters to predict whether the budget will pass. Suppose the budget has the support of 52% of the voters. What is the probability that the newspaper's sample will lea predict defeat?

Dana Hills High School was considering going back to campus rather than remote instruction for the remainder of the semester. To make this decision, the school sent out a survey to students, parents, teachers, and staff to see if they would prefer remote or on campus instruction. The results of the survey are given in the table below. Find the probability that a person has no preference or is a student. Student Parent Teacher Staff TOTAL Remote 54 78 59 36 227 On-Campus 79 82 37 55 253 No Preference 23 12 11 54 ТОTAL 156 172 104 102 534 0.406 O 0.393 O 0.350 0.327 0.311

A cooler contains 100 ice cream bars. There are 30 Vanilla​ bars, 20 Mint Chocolate Chip​ bars,10 Chocolate​ bars, and 40 Rocky Road bars. If one bar is selected at random from the​ cooler, determine the probability that the bar selected is Vanilla​, Chocolate​, or Rocky Road.

Jordan went to shelter to adopt a dog. There were 10 brown dogs and 10 black dogs. Jordan picked a dog, went home, then decided he wanted to go back and adopt another dog. What is the probability that he picked two black dogs?

A social scientist gathers a carefully chosen group of 20 people whom she is selected to represent a broad cross section of the multiple of the population in New York City. She interviews them in depth for a study that she is doing regarding race relations in the city. Is there a probability sample? Explain your answer.

Below are the numbers of patients classified as underweight, normal weight, overweight and obese according to their diabetes status.  If a patient is selected at random: What is the probability that they are overweight? What is the probability that they are obese and diabetic? What proportion of the diabetics are obese? What proportion of normal weight patients are not diabetic? What proportion of patients are normal weight or underweight?     Underweight Normal Weight Overweight Obese Row Totals   Diabetic 8 34 65 43     Not Diabetic 12 85 93 40     Column Totals

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.