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 10.3. 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 493. The probability that a randomly selected medical student who took the test had a total score that was less than 493 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 500 and 515. The probability that a randomly selected medical student who took the test had a total score that was between 500 and 515 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.)

A sample of n = 15 scores has a mean of M = 6.  One person with a score of X = 22 is added to the sample. What is the value for the new sample mean?

A rugby team from the country of Atlantis is formed by randomly drawing from its population. The population distribution is normally distributed with a mean of 165 cm and a standard deviation of 10 cm. The team draws 26 people for the team. What is the probability that the sample mean is less than 163? Give your answer to four decimal places.

What formula do I use?

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1511 and the standard deviation was 312. The test scores of four students selected at random are 1910, 1280, 2240, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1910 is (Round to two decimal places as needed.) The z-score for 1280 is (Round to two decimal places as needed.) The Z-score for 2240 is (Round to two decimal places as needed.) The Z-score for 1420 is (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice OA. The unusual value(s) is/are (Use a comma to separate answers as needed.) OB. None of the values are unusual.

Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?

The board of examiners that administers the real estate broker’s examination in a certain state found that the mean score on the test was 450 and the standard deviation was 50.  If the board wants to set the passing scores so that only the top 5% of all applicants pass, what should the passing score be?  Assume that the scores are normally distributed.

The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?

The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 494 and the standard deviation was 72. If the board wants to set the passing score so that only the best 10% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. Round to the nearest whole number.

The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 20. What is the probability we could select a sample of 20 adults and find the mean of this sample is less than 95? 0.1314 0.7372 0.3686 0.7098