Question 10

For the standard normal probability distribution, the area to the left of the mean is

(a) None of the above

(b) 0.5

(c) Greater than 0.5

(d) Less than 0.5

Question 11

The travel time for a tourist traveling between Johannesburg and Cape Town is uniformly distributed between 720 and 840 minutes. The probability that he will finish his trip in 800 minutes or less is approximately:

(a) 50%

(b) 80%

(c) 67%

(d) 33%

Question 12

A standard normal distribution is a normal distribution with the following parameters:

(a) Mean of 0 and standard deviation of 1

(b) Any mean and any standard deviation

(c) Mean of 0 and standard deviation of 0

(d) Mean of 1 and standard deviation of 0

Question 13

A garage would like to know what percentage of their store's customers' cars have low oil pressure. Over a year 500 vehicles are randomly chosen and the oil pressure is recorded. A total of 120 of the cars measured have low oil pressure. The estimate population proportion of cars with low oil pressure is:

(a) 42%

(b) 24%

(c) 20%

(d) 50%

Question 14

If a scatter plot shows a negative relation between two variables X and Y then, in general, as

(a) None of the above

(b) X decreases, Y increases

(c) X decreases, Y decreases

(d) X increases, Y increases

Question 15

A researcher is curious about the IQ of students at UNZA and decides to carry out an experiment. In this context, the entire group of students is an example of a:

(a) Statistic

(b) Population

(c) Parameter

(d) Sample

Question 16

A researcher is curious about the IQ of students at UNZA and decides to carry out an experiment. IQ test results are standardized so that the mean score is 100 for all test takers. Nevertheless, if you select any group of 50 students who took the test the result would probably be different than 100. What concept explains the difference between the two means?

(a) None of the above

(b) Parametrical error

(c) Residual error

(d) Sampling error

Question 16

Which of the following Z-scores is the closest to the mean of the distribution:

(a) Z = - 0.4

(b) Z = + 1.2

(c) Z = - 1.1

(d) Z = + 0.6

Question 17

If the scores on a test have a mean of 40 and a standard deviation of 8, what is the z-score for a score of 16?

(a) -3

(b) 4

(c) 5

(d) 3

Question 18

What does a slope of 1.5 represent in a linear regression equation?

(a) For every increase in one unit of x, y increases by 1.5 units

(b) For every increase in one unit of y, x increase by 1.5 units

(c) For every increase in one unit of y, x decreases by 1.5 units

(d) For every increase in one unit of x, y increases by 15 units

Question 19

Suppose the coefficient of determination r²in a linear regression of height and weight for adults is 0.46. What proportion of the variability in weight cannot be explained by the relationship with height?

(a) 54%

(b) 68%

(c) 36%

(d) 46%

Question 20

You buy a package of 150 M&Ms and 25 of them are yellow. What is the 95% confidence interval for the true proportion of yellow M&Ms?

(a) (0.16, 0.18)

(b) (0.11, 0.23)

(c) (0.12, 0.22)

(d) (0, 0.90)

Question 21

The expected value of the probability distribution of X is 24 and the standard deviation is 16. If the random variable Y can be written as Y = 2.5X - 10, then the standard deviation of Y is

(a) 40

(b) 60

(c) 100

(d) 30

Question 22

An electronic circuit is made of three components, X, Y and Z. The probabilities of failure for each component in any one month is 1.8%, 1.5%, and 2.1%, respectively. If any one component fails, the circuit will fail. If the components fail independently, what is the probability that the circuit will not fail in one month?

(a) 89%

(b) 99.9%

(c) 92.1%

(d) 94.7%

Question 23

In a city in England a program exists to encourage more college students to select STEM courses when they go to University. Researchers want to estimate the proportion of students who, after completing the program, take STEM subjects in University. The researchers selected a sample of 100 students from all students who completed the program. Which of the following best describes a stratified random sample?

(a) Select every 5-th student from the list of students

(b) Randomly select 100 students.

(c) Randomly select 100 male students.

(d) Randomly select 50 male students and randomly select 50 female students.