uppose a simple random sample of size n=150 is obtained from a population whose size is N=15,000 and whose population proportion with a specified characteristic is p=0.8. What is the probability of obtaining x=114 or fewer individuals with the​ characteristic? That​ is, what is ​P(p≤0.76​)?

Suppose that a random sample of size 25 is to be selected from a population with mean 46 and standard deviation 8. What is the approximate probability that X will be more than .5 away from the population mean?

The president of Doerman Distributors, Inc., believes that 28% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.  What is the probability that the sample proportion will be between 0.16 and 0.40 (to 4 decimals)? What is the probability that the sample proportion will be between 0.21 and 0.35 (to 4 decimals)?

Suppose you are a lawyer representing a Hispanic individual in a criminal trial. Twelve jurors are randomly selected by the state from a population that you know to be 40% Hispanic. 4.8 JURORS ARE EXPECTED TO BE HISPANIC. The select process produces a jury with 3 Hispanic individuals, meaning that 25% of the jury is Hispanic. Using the binomial distribution we find that the probability that 3 or fewer jurors would be Hispanic is 0.2253. Create a graph of the distribution with the area corresponding to the previous information.   Use Statistics to make an argument to the court on behalf of your client. Explain why random sampling in this situation of juror selection relates the expected sample proportion to the population proportion.Compare the expected value to the actual sample proportion.

Suppose that from the past experience a professor knows that the test score of a student taking his final examination is a random variable with mean 61 and a standard deviation 8.5. how many students would have to take the examination to ensure, with probability at least 0.94, that the class average would be within 3 of 61?

Suppose that 70% of Americans support the death penalty for persons convicted of murder. Let p> (p hat) be the sample proportion of proportion of people who support the death penalty in an SRS of Americans.  Suppose we set our sample size to be n=84. What is the probability of choosing an SRS in which between 65% and 73% of the people in the people in the sample support the death penalty? That is, find P(0.65<p(phat)<0.73). Show your work and box your answer.

A doctor is interested in the proportion of patients which live at least 5 years after being diagnosed with stage 4 breast cancer. He randomly selects 138 patients diagnosed with stage 4 breast cancer and follows them for 5 years. Suppose the true 5 year survival rate for stage 4 breast cancer is 38%. 1. How are the collection of all sample proportions of samples of size 138 distributed? NO 2. What is the probability that fewer than 34% of the patients studied survived for at least 5 years? o List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. o There is a survived for at least 5 years. 3. What is the probability that more than 45% of the patients studied survived for at least 5 years? chance that fewer than 34% of the patients studied o List the z-scores needed to calculate the result. If there is more than one z-score, separate the values with a comma. O There is a survived for at least 5 years. chance that more than…

I. Boston Children’s Hospital estimates that 90% of Americans have had chickenpoxby the time they reach adulthood.32(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distributionappropriate for calculating the probability that exactly 97 out of 100 randomly sampled Americanadults had chickenpox during childhood? Explain.(b) Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpoxduring childhood.(c) What is the probability that exactly 3 out of a new sample of 100 American adults have not hadchickenpox in their childhood?(d) What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox?(e) What is the probability that at most 3 out of 10 randomly sampled American adults have not hadchickenpox?

What is the probability of obtaining a z score that is as extreme as or more extreme than 1.96?

Suppose weights, in pounds, of dogs in a city have an unknown distribution with mean 31 and standard deviation 5 pounds. A sample of size n=39 is randomly taken from the population and the sum is taken. What is the probability that the resulting sum is between 1180 and 1194 pounds?