1. A manufacturer sends out 1000 lots each consisting of 100 electric bulbs. If 5% of the bulbs are normally defective in how many of the lots should we expect (a) fewer than 90 good bulbs and (b) 98 or more good bulbs?SAMPLING DISTRIBUTIONS OF DIFFERENCES AND SUMS2. A and B manufacture two types of cables that have mean breaking strengths of 4000 lb and 4500 lb and standard deviations of 300 lb and 200 lb respectively. If 100 cables of brand A and 50 cables of brand B are tested what is the probability that the mean breaking strength of B will be (a) at least 600 lb more than A and (b) at least 450 lb more than A?3. What are the probabilities in Problem 8.40 if 100 cables of both brands are tested? Account for the differences.4. The mean score of students on an aptitude test is 72 points with a standard deviation of 8 points. What is the probability that two groups of students consisting of 28 and 36 students respectively will differ in their mean scores by (a) 3 or more points (b) 6 or more points and (c) between 2 and 5 points?5. An urn contains 60 red marbles and 40 white marbles. Two sets of 30 marbles each are drawn with replacement from the urn and their colors are noted. What is the probability that the two sets differ by 8 or more red marbles?