Super Bowl: In 2018 it was estimated that approximately 45% of the American population watches the Super Bowl yearly. Suppose a sample of 120 Americans is randomly selected. After verifying the condition for the Central Limit Theorem are met, find the probability that a majority (more than 50%) watched the super Bowl. Verify that the conditions for the Central Limit Theorem for Sample Proportions have been met: (met or not met) 1) Random and Independent: Is the sample collected randomly and the trials are independent from each other? (met or not met) 2) Large Sample: Is there at least 10 successes and at least 10 failures? (met or not met)

Given a normally distributed population with a mean of 100 and variance of 400, find the following probabilities for a sample mean for 16 individuals: a) P(X> 100) b) P(X ≤ 110) c) P(96 ≤ X ≤ 108)

When using the central limit theorem for means with n = 98, it is not necessary to assume the distribution of the population data is normally distributed. True False

Suppose 10% of students are veterans. From a sample of 279 students, how unusual would it be to have less than 20 veterans?Is the success-failure condition of the Central Limit Theorem satisfied? A) No. Either np < 10 or n(1−p) < 10. B) Yes. Both np and n(1−p) are ≥10. The Central Limit Theorem tells us that the distribution of sample proportions approximately follows a _______ distribution with mean ____ and standard deviation _____ .Given this knowledge, use technology to compute the probability that, through random selection, one finds a sample proportion that is less than the proportion corresponding to 20 veterans.Round answer to 4 decimal places. Is this result unusual? A) Yes. There is a less than 5% chance of this happening by random variation. B) No. There is at least a 5% chance of this happening by random variation.

According to recent data, 45% of the U. S. adults have hypertension. A random sample of 750 adults in the U.S. is selected. Let X represent the number that have hypertension. a. Under what condition will this binomial distribution be bell-shaped? State this condition and verify that that condition is met here. Show the calculation required.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the x distribution is about $46 and the estimated standard deviation is about $9.   (a) MULTIPLE CHOICE Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? A-The sampling distribution of x is approximately normal with mean ?x = 46 and standard error ?x = $0.23. B-The sampling distribution of x is not normal. C-The sampling distribution of x is approximately normal with mean ?x = 46 and standard error ?x = $1.42. D-The sampling distribution of x is approximately normal with mean ?x = 46 and standard error ?x = $9. (MULTIPLE CHOICE)Is it…

Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value  has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of  x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.

When presented with fingerprints from the same individual, a fingerprint expert will correctly identify the match 94% of the time, Suppose a random sample of 110 was collected and you were asked to find the probability that more than 90% of the fingerprints were correctly idenfied. Which one of the following conditions for the Central Limit Theorem (CLT) is not met? O a. The expected number of "successes" in the sample is too small. O b. The expected number of "failures" in the sample is too small. O,. Relative to the size of the sample, the population is not large enough. O d.A non-random sample was collected.

When using the Central Limit Theorem, what is the "magic number" for sample size that allows you to use the C.L.T even if the population is not normally distributed?

The billing department of a local department store sends monthly statements to the store’s customers. For those statements to reach the customer in a timely fashion, the addresses on the envelopes must be correct. Occasionally errors are made with the addresses. The billing department estimates that errors are made 2 percent of the time. For this continuous process, in which an error in the address is considered a nonconforming unit, what is the probability that in a sample size of eight, one address or less will be incorrect?