Question 1: Which of the following is true for any density curve?
a. It is symmetric.
b. The total area under the curve is 1.
c. It must either steadily rise or steadily fall. It cannot do both.
d. Bars must be of equal width.
Question 2: A normal density curve has which of the following properties?
a. It is symmetric.
b. It has a peak centered above its mean.
c. The spread of the curve is proportional to the standard deviation.
d. All of the above.
Question 3: A company produces ceramic floor tiles that are supposed to have a surface area of 16.0 square inches. Due to variability in the manufacturing process, the actual surface area has a normal distribution with a mean of 16.1 square inches and a standard deviation of 0.2 square inches. The proportion of tiles produced by the process with surface area less than 16.0 square inches is
a. 0.1915
b. 0.4115
c. 0.3085
d. 0.6915
e. -0.3085
Question 4: Weight of the chocolate bars produced by a certain machine is normal with a mean of 8.1 oz. and a standard deviation of 0.1 ounces. The proportion of chocolate bars with weights between 8.2 and 8.3 oz. is
a. 0.819
b. 0.636
c. 0.477
d. 0.136
e. 0.089
Question 5: The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the top 15% of students are given A's, what is the lowest mark that a student can have and still be awarded an A?
a. 51
b. 74
c. 90
d. 93
e. 95
Question 6: Let X denote the time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site. It is known that X has a normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. On 90% of the occasions the computer link is made in less than
a. 19.39 seconds.
b. 15.95 seconds.
c. 11.16 seconds.
d. 18.84 seconds.
e. 22.11 seconds.
Question 7: An incoming freshman took her college's placement exams in French and mathematics. In French she is scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation 8, while the mean math score was 68, with a standard deviation of 12.
On which exam did she do better compared with the other freshmen?
a. On French.
b. On Mathematics.
c. There is not enough information to answer the question.
Question 8: Some IQ test are standardized to a Normal model, with a mean of 100 and a standard deviation of 16.
a) About what percent of people should have IQ scores above 132?
b) About what percent of people should have IQ scores between 68 and 84?
c) About what percent of people should have IQ scores above 116?
d) In what interval would you expect the central 95% of IQ scores to be found?
Question 9: IQs revisited. Based on the Normal model N(100, 16) describing IQ scores, what percent of people's IQs would you expect to be
a) between 112 and 132?
b) over 80?
c) under 90?
Question 10. More IQs. In the Normal model N(100, 16), what cut-off value bounds
a) the highest 5% of all IQs?
b) the lowest 30% of all IQs?
c) the middle 80% of all IQs?