A variation of a roulette wheel has slots that are not of equal size. Instead, the width of any slot is proportional to the probability that a standard normal random variable z takes on a value between a and (a + .1), where a = –3.0, –2.9, –2.8, . . . , 2.9, 3.0. In other words, there are slots for the intervals through (–3.0, –2.9), (–2.9, –2.8), (–2.8, –2.7) through (2.9, 3.0). There is one more slot that represents the probability that z falls outside the interval (–3.0, 3.0). Find the following probabilities.
a. The ball lands in the slot representing (.3, .4).
b. The ball lands in any of the slots representing (–.1, .4).
c. In at least one out of five games, the ball lands in the slot representing (–.1, .4).
d. In at least 100 out of 500 games, the ball lands in the slot representing (.4, .5).