Question: (6 pt) Infants weighing less than 1500 grams at birth are classed as "very low birth weight". Low birth weight carries many risks. One study followed 113 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was

\(\bar{X}=\) 87.6. IQ scores vary normally with standard deviation \(\sigma =\) 15.

a. (2 pt) Give a 95% confidence interval for the mean IQ score at age 20 for all very low birth weight males and state it in terms of the problem.

b. (2 pt) How many infants would you need to sample to reduce the margin of error to just 2 IQ points at the 95%confidence level?

c. (2 pt) The mean IQ score for normal adults is 100. What is the probability that the average score of 10 adults would be less than the mean score of the low birth weight adults (87.6)?