A company đětěrm that on an anhual basIs, the distance traveled per company car is normally distributed with a mean of 50,000 miles and a standard deviation of 12,000 miles. a. What proportion of cars can be expected to travel between 34,000 and 50,000 miles in a year? b.What is the probability that a randomly selected car travels between 34,000 and 38,000 miles? c. How many miles will be traveled by at least 80% of the cars?

The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. a. In a letter to an advice​ column, a wife claimed to have given birth 307 days after a brief visit from her​ husband, who was working in another country. Find the probability of a pregnancy lasting 307 days or longer. What does the result​ suggest? b. If the length of pregnancy is in the lowest 3​%, then the baby is premature. Find the length that separates premature babies from those who are not considered premature.       a. The probability that a pregnancy will last 307 days or longer is enter your response here. ​(Round to four decimal places as​ needed.) What does the result​ suggest?     A. The result suggests that either a very rare event occurred or the husband is not the father.   B. The result suggests an uncommon but not significant event occurred.   C. The result suggests the event did not occur.   D. The result suggests that the…

O 6. Salaries for Actuaries The average salary for gradu- ates entering the actuarial field is $63,000. If the salaries are normally distributed with a standard deviation of $5000, find the probability that a. An individual graduate will have a salary over $68,000. b. A group of nine graduates will have a group average over $68,000. Source: www.payscale.com & 7. Commuter Train Passengers On a certain run of : commuter train, the average number of passengers is 476 and the standard deviation is 22. Assume the variable is normally distributed. If the train makes the run, find the probability that the number of passengers will be a. Between 476 and 500 passengers b. Fewer than 450 passengers c. More than 510 passengers

Sixty-two percent of seniors attend a particular school in a school district. Assume 500 seniors within this school district are sampled. a. Can this distribution be approximated using the Normal model? Explain. b. Use the Normal approximation to estimate the probability that at least 290 senior students are enrolled at this particular school. c. Use the Normal model to estimate the probability that between 200 and 300 senior students who are sampled are enrolled at this particular school.

6. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. a. Find the probability that a single can of Coke has at least 12.19 oz. b. Find the probability that a pack of 36 cans of Coke have a mean of at least 12.19 oz. c. Suppose you measured the cans of a random 36-pack and got a sample mean of 12.19 oz. Is it reasonable to assume that the actual population mean is 12.00 oz? Why or why not?

K A survey found that women's heights are normally distributed with mean 63.4 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements? Click to view page 1 of the table. Click to view page 2 of the table. correct: 1 C... a. The percentage of women who meet the height requirement is (Round to two decimal places as needed.)

Assume that the sales of Teri’s Specialty Cakes has historically followed a normal distribution, with an average of 250 cakes per month, and a standard deviation of 15 cakes.a. What is the probability that the sales for cakes will be no more than 285 over the next month?b. What is the probability that the sales for the cakes will be no more than 230 cakes over the next month?c. What is the probability that the sales for the cakes will be between 245 and 265 over the next month?d. What number of cake demand can Teri reasonably assume with a confidence level of 95%?For a, b, c, and d, please write out your work for at least one of these problems. For all problems, explain your answers and sketch a plot (similar to the handouts and text).

In a distribution with a mean of 80 and a standard deviation of 8, what percentage of number would be: a. Less than 64 or greater than 96 b. Less than 60 or greater than 100 c. Less than 52 or greater than 108