# Exam Exam

1.- A company has a total of 360 employees in four different categories:
Managers: 36
Drivers: 54
Production Staff: 180

How many from each category should be included in a stratified random sample of size 20 ?

 a) 2, 4, 4 and 10 b) 2, 3, 6 and 9 c) 2, 3, 5 and 10 d) None of them

2.- A farmer owns 120 Jersey cows and 180 Friesians. How many cows of each breed should he include in a stratified random sample of 50 for a survey of milk quality?

 a) 20 and 30 b) 22 and 28 c) 15 and 35 d) None of them

3.-  If a random variable has the normal distribution with μ= 82.0 and σ= 4.8, find the probabilities that it will take on a value between 83.2 and 88.0

 a) 0.2957 b) 0.3944 c) 0.2734 d) None of them

4.- Scientists study a large fish population. The mean fish length is 50 cm and the SD is 26 cm. If a sample of 169 fish is randomly selected, what is the probability that the sample's mean is between 46 and 48 cm?

 a) 0.2734 b) 0.1359 c) 0.2552 d) None of them

5.- The numerical population of grade point averages at a college has mean 2.61 and standard deviation 0.05. If a random sample of size 100 is taken from the population, what is the probability that the sample mean will be between 2.51 and 2.71?

 a) 0.9772 b) 0.9544 c) 0.9192 d) None of them

6.- According to data from the American Cancer Society, about 3.86% of women develop breast cancer between the ages of 40-59.

What is the probability that, in a random sample of 500 39-year-old women without breast cancer, more than 20 will develop breast cancer by the age of 60?

 a) 0.5636 b) 0.4602 c) 0.4364 d) None of them

7.- In a typical class, about 70% of students receive a C or better. Out of a random sample of 100 students, what is the probability that less than 60 receive a C or better?

 a) 0.0179 b) 0.0139 c) 0.015 d) None of them

8.- For boys, the average number of absences in the first grade is 15 with a standard deviation of 7; for girls, the average number of absences is 10 with a standard deviation of 6.

In a nationwide survey, suppose 100 boys and 50 girls are sampled. What is the probability that the male sample will have at most three more days of absences than the female sample?

 a) 0.035 b) 0.0359 c) 0.0287 d) None of them

9.- In a study to compare the average weights of children in Sixth Grade at an elementary school, a random sample of 20 boys and one of 25 girls will be used. It is known that, both for boys and for girls, weights follow a normal distribution. The average of the weights of all the boys in Sixth Grade in that school is 100 pounds and its standard deviation is 14.142, while the average of the weights of all the girls in sixth grade in that school is 85 lbs and its standard deviation is 12.247 pounds. Find the probability that the average of the weights of 20 boys is at least 20 pounds bigger than the one of 25 girls.

 a) 0.1151 b) 0.1056 c) 0.0968 d) None of them

10.- Decide which of the following sentences is false

 a) Point estimation consists in estimating the unknown population parameter by a unique value b) Inside inferential statistics we find inductive statistics, which estimate the population parameters through the sample ones c) Sample mean is the unbiased estimate of the population mean d) Sample mean is the unbiased estimate of the population proportion