STATISTICS

1. Find the area under the standard normal curve between z = -1.9 and

z = 1.8.

2. Assume that X has a normal distribution, with mean, f$mu= 17 f$ , and standard deviation, f$sigma = 3 f$ . Find P(7

3. 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)?

4. A cement truck delivers mixed cement to a large construction site. Let X represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction site with another load of cement. From past experiences, it is known that the mean cycle time is 41 minutes with a standard deviation of 13 minutes and that cycle times are normally distributed. What is the probability that the cycle time will exceed 48 minutes, given that it has exceeded 39 minutes?

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 f$hat{p}= frac{r}{n}f$is the proportion of defective toys in a lot. Find f$P(.07leq hat{p}leq .09)f$ . 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 is, find f$P(7leq rleq 9)f$.