For the following questions, you don't need to use any data sets. You need to use appropriate statistical and probability functions covered in lecture 9 to answer the following questions.

a. Birth weights at a local hospital have a normal distribution with a mean of 100 oz. and a standard deviation of 5 oz. What is the proportion of infants with birth weights between 125 oz. and 140 oz., P(125 < x < 140)? (2 pts)

b. The scores on a university examination are Normally distributed with a mean of 60 and a standard deviation of 6. What is the score that represents 5^th percentile of the distribution?(2 pts)

c. Each child born to a set of parents has a probability of 0.5 of being male or female.Suppose a particular set of parents have 5 children. What is the probability thatexactly 3 of them are boys P(x=3)? What is the probability thatless than 3 of them are boy P(x2)? (4 pts)