To compute P(X < 7) for a binomial distribution, what would be an equivalent notation? О а. 1- Р(X < 6) O b. 1- P(X < 7) O c. P(X < 6) O d. P(X s 7)

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.

Assume that when human resource.managers are randomly selected, 42% say job applicants should follow up within two weeks. If 15 human resource managers are randomly selected, find the probability that fewer than 3 of them say job applicants The probability is should follow up within two weeks.

It is known that 37% of new freshmen at State University will graduate within 6 years. Suppose we take a random sample of n=70 new freshmen at State University. Let X = the number of these sampled freshmen who graduate within 6 years. (Do not use a normal approximation for this problem. This is a binomial problem.) a) What is the probability that X < 29? b) What is the probability that 28 ≤ x ≤ 31? c) What is the probability that X = 31? d) What is the expected value of X? e) What is the variance of X?

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.