Question 1. The scores on a college entrance exam have an approximate normal distribution with mean, I1 = 52 points and a standard deviation, 0' = 11 points. [a] About 68% ofthe 3} values lie between what two values? These values are . The 2- scores are , respectively. {b} About 95% ofthe 3} values lie between what two values? These values are . The :- scores are , respectively. {c} About 99.7% of the y values lie between what two values? These values are The zscores are respectively. Question 2. Height and weight are two measurements used to track a child's development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean u = 10.2 kg and standard deviation 0 : 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them. [a] 11 kg {b} 7.9 kg {c} 12.2kg Question 3. lfz is the standard normal variable, find: (Include a sketch of the graph} {a} P(2.04 1.77) Question 4. 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. [a] What is the probability of spending more than two days in recovery? Include a sketch of the graph. {b} What is the probability of spending between 3 and 4 days in recovery? Include a sketch of the graph. Question 5. lQis normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. LetX = IQ of an individual. a. X ~ __(__, _) b. Find the probability that the person has an IQ greater than 120. Include a sketch of the graph. c. Find the probability that the person has an IQ less than 110. Include a sketch of the graph