There are 40 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 6 min and a standard deviation of 6 min.a. If grading times are independent and the instructor begins grading at 6:50 p.m. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 p.m. TV news begins?b. If the sports report begins at 11:10, what is the probability that he missespart of the report if he waits until grading is done before turning on the TV?

Suppose the heights of 18 year old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches. What is the probability that an 18 year old man selected at random is between 70 and 72 inches tall?  if random sample of twenty-nine 18 year old men is selected, what is the probability that the mean height x is between 70 and 72 inches?  compare your answers to parts a and b. Is the probability in part b much higher? Why

Among all monthly bills from a certain credit card company, the mean amount billed was $465 and the standard deviation was $300. In addition, for 15% of the bills, the amount billed was greater than $1000. A sample of 900 bills is drawn.     What is the probability that more than 150 of the sampled bills are for amounts greater than $1000? (Round the final answer to four decimal places.)

3. Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is between a 6 and a 9?

The U.S. Fish and Wildlife Service reported that the lengths of six-year-old rainbow trout in the Arolik River in Alaska are normally distributed with a mean of 481 millimeters and standard deviation of 41 millimeters. If a six-year-old rainbow trout from the Arolik River is selected at random, what is the probability it's length is more than 500 millimeters?   Question 5 options:   0.1588   0.3215   0.4576   0.6785

The distribution of weekly salaries at a large company has a mean of $1000 and a standard deviation of $350. What is the probability that the mean of a random sample of weekly salaries of 50 employees will be at most $900? 0.0217 O 0.9783 O 0.3438 O Cannot be determined, because the distribution of the population is not normal.

The median annual cost of auto insurance is $ 939 (According to DACO). Suppose the standard deviation is o = $ 241. What is the probability that in a simple random sample of auto insurance policies the sample mean differs more than $ 70.42 from the population mean if the sample size is 45? You must calculate the probability that the difference between the average cost in the sample and the average annual cost do not differ by $ 70.42. Find the probability that P (\ µ - š | 0) = P (-70.42 H-iS 70.42) Select one: a. The probability is 99% that the auto policy will not differ by $ 70.42 from the average annual cost. b. The probability is 50% that the auto policy will not differ by $ 70.42 from the average annual cost. c. The probability is 80% that the auto policy will not differ by $ 70.42 from the average annual cost. d. The probability is 70% that the auto policy will not differ by $ 70.42 from the average annual cost. e. The probability is 95% that the auto policy will not differ by $…