On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 115 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected person's IQ is over 101. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 4% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.5 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. What is the median recovery time? days c. What is the Z-score for a patient that took 5.6 days to recover? d. What is the probability of spending more than 3.1 days in recovery? e. What is the probability of spending between 3.6 and 4.5 days in recovery? f. The 85th percentile for recovery times is days.

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