Normal distribution

1. The average American man consumes 9.7 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.9 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(__,____) b. Find the probability that this American man consumes between 9.8 and 10.6 grams of sodium per day. ? c. The middle 30% of American men consume between what two weights of sodium? Low: High:
2. The mean amount of time it takes a kidney stone to pass is 15 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. 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 with a kidney stone will take longer than 14 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.
3. On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 119 and a standard deviation of 17. 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 80. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 5% 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:
4. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.8 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 4.8 days to recover? d. What is the probability of spending more than 3.4 days in recovery? e. What is the probability of spending between 2.3 and 3.2 days in recovery? f. The 80th percentile for recovery times is days?