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A normal distribution has a mean of 61 and a standard deviation of \(15 .\) What is the median?

What is the z-score of \(x=12,\) if it is two standard deviations to the right of the mean?

Suppose \(X \sim N(9,3) .\) What is the \(z\) -score of \(x=9 ?\)

If the area to the left of x in a normal distribution is 0.123, what is the area to the right of x?

Use the following information to answer the next four exercises: X ~ N(54, 8) Find the \(80^{\text { th }}\) percentile.

\(X \sim N(4,5)\) Find the maximum of \(x\) in the bottom quartile.

Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. The heights of the 430 National Basketball Association players were listed on team rosters at the start of the 2005–2006 season. The heights of basketball players have an approximate normal distribution with mean, ? = 79 inches and a standard deviation, ? = 3.89 inches. For each of the following heights, calculate the z-score and interpret it using complete sentences. a. 77 inches b. 85 inches c. If an NBA player reported his height had a z-score of 3.5, would you believe him? Explain your answer.

Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean ? = 520 and standard deviation ? = 115. a. Calculate the z-score for an SAT score of 720. Interpret it using a complete sentence. b. What math SAT score is 1.5 standard deviations above the mean? What can you say about this SAT score? c. For 2012, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 5.3. If one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 30, who did better with respect to the test they took?

Use the following information to answer the next three exercises: The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space? a. Yes b. No c. Unable to determine