1. Find the area under the standard normal curve between z = -1.9 and z = 1.8.
2. Let z be a random variable with a standard normal distribution. Find P(-2.9 < z < 0.4).
3. Assume that X has a normal distribution, with mean, , and standard deviation, . Find P(7 < X < 18).
4. A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 56 months and a standard deviation of 6 months. If the company does not want to make refunds for more than 10% of its batteries under a full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
5. Assume that 55% of all customers will take free samples. Furthermore, of those who take the free samples, assume that about 32% will buy what they have sampled. Suppose that you set up a counter in a supermarket offering free samples of a new product and that the day you were offering free samples, 347 customers passed by your counter. What is the probability that a customer will take a free sample and buy the product?
6. The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of twenty 18-year-old men will be less than 69 inches?
7. A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it still produces about 8% defective toys. The toys are manufactured in lots of n = 100. Let r be a random variable representing the number of defective toys in a lot. Then is the proportion of defective toys in a lot. Find . Round your answer to four decimal places.
8. A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it still produces about 8% defective toys. The toys are manufactured in lots of n = 100. Let r be a random variable representing the number of defective toys in a lot. Find the probability that between 7 and 9 defective toys are produced in a lot of n = 100 toys. That
