**MATH530 Applied Statistics **

**Quiz 2**

Question 1 Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches, what percentage of women are taller than 67.5 inches?

Question options:

0.1%

15.9%

97.7%

50.0%

84.1%

Question 2 Find the area under the standard normal curve between z = -1.9 and z = 1.8.

Question options:

0.036

0.471

0.029

0.964

0.935

Question 3 Let z be a random variable with a standard normal distribution. Find P(-2.9 < z < 0.4).

Question options:

0.994

0.654

0.002

0.498

0.155

Question 4 Assume that X has a normal distribution, with mean, , and standard deviation, . Find P(7 < X < 18).

Question options:

0.999

0.369

0.001

0.630

1.000

Question 5 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)?

Question options:

56 months

67 months

48 months

44 months

63 months

Question 6 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?

Question options:

0.526

0.297

0.565

0.295

0.561

Question 7Assume 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?

Question options:

0.320

0.582

0.230

0.176

0.550

Question 8The 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?

Question options:

0.0968

0.4032

0.8064

0.9320

0.4516

Question 9A 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.

Question options:

0.2719

0.7719

0.2281

0.2085

0.2876

Question 10 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 .

Question options:

0.2719

0.7719

0.4188

0.2085

0.5812