11. In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.8. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 486. The probability that a randomly selected medical student who took the test had a total score that was less than 486 is (Round to four decimal places as needed.) (b) Find the probability that a randomly selected medical student who took the test had a total score that was between 495 and 510. The probability that a randomly selected medical student who took the test had a total score that was between 495 and 510 is (Round to four decimal places as needed.) (c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 527. The probability that a randomly selected medical student who took the test had a total score that was more than 527 is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. OA. None of the events are unusual because all the probabilities are greater than 0.05. OB. The event in part (a) is unusual because its probability is less than 0.05. OC. The event in part (c) is unusual because its probability is less than 0.05. D. The events in parts (a) and (b) are unusual because their probabilities are less than 0.05.

The percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)

The average amount of money spent for lunch per person in the college cafeteria is $5.99 and the standard deviation is $2.1. Suppose that 49 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. For the group of 49 patrons, find the probability that the average lunch cost is between $5.77 and $6.08.

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 64 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 57 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes

n a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 21 scores from all of the students who took the test. She sees that the mean score is 128 with a standard deviation of 41.4416. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 25. Is there evidence that the standard deviation of test scores has increased at the α=0.005 level? Assume the population is normally distributed. Step 1 of 5 :  State the null and alternative hypotheses. Round to four decimal places when necessary.

Suppose a batch of steel rods produced at a steel plant have a mean length of 178 millimeters, and a standard deviation of 12 millimeters. If 76 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.56 millimeters? Round your answer to four decimal places.

r a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of  510  and a standard deviation of  170 . The grading process of this year's exam has just begun. The average score of the  40  exams graded so far is  526 . What is the probability that a sample of  40  exams will have a mean score of  526  or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.