1. Let x denote the IQ for an individual selected at random from a certain population. The value of x must be a whole number. Suppose that the distribution of x can be approximated by a normal distribution with mean value 100 and standard deviation 15. Approximate the following probabilities:
a. P(x = 100) b. P(x 110)
c. P(x 110) (Hint: x 110 is the same as x 109.) d. P(75 x 125)
2. Suppose that the distribution of the number of items x produced by an assembly line during an 8-hour shift can be approximated by a normal distribution with mean value 150 and standard deviation 10.
a. What is the probability that the number of items produced is at most 120?
b. What is the probability that at least 125 items are produced?
c. What is the probability that between 135 and 160 (inclusive) items are produced?