Exercises 5.10: 30, 40(a)(b), 44, 46, 47, 48, 49, 50, 51(a), 54

Hint: 49 will help with 48(b).

Note: use the table to find the normal probabilities in the exercises.

Also:

1. Suppose the lifetime of a certain tire has a normal distribution with mean 50,000 miles and standard deviation 5000 miles. Find:
   1. The probability that a tire will last between 48,000 and 56,000 miles.
   2. Find the value $a$ such that the probability that a tire lasts more than $a$ miles is approximately 0.8.
2. Suppose a the lifetime of a certain type of fuse has an exponential distribution with mean 5,000 hours.
   1. Find the probability that a fuse will last more than 8,000 hours.
   2. Find the value $a$ such that the probability that a fuse will last less than $a$ hours is 0.95.

For Problem Set due 2 November: 47, 54

Answers:

1. (a) 0.5403 (b) 45,800
2. (a) 0.2019 (b) 14,979