TEST 4 STATISTICS

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?

0.

A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?

0.0195

Mrs. Boyette has spent some of lonely time in the school building studying the cockroaches that inhabit Sanderson. She has learned the weight of the roaches is approximately normal with mean 25 grams and standard deviation 4 grams. Which of the following is closest to the proportion of roaches with a weight greater than 33 grams?

0.023

The probability that a new microwave will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

0.40

A die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die 3 times before blue lands faceup.

0.5625

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, what is the age of a Galápagos Islands giant tortoise at the 90th percentile of the distribution? Round to the nearest whole number.

119

Ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. Ninety percent of the people who do not have the disease will have a negative result on this test. If 5 percent of a certain population has the disease, what percent of that population would test positive for the disease? Enter your answer as a whole number. Do not include the "%" sign.

14%

The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y? Enter whole numbers.

22m and 100sd

A probability experiment involves a series of identical, independent trials with two outcomes (success/failure) per trial and the probability of a success on each trial is 0.2. Determine the number of trials, n, in a binomial experiment such that the expected number of successes in that binomial experiment will be equal to the expected number of trials in a geometric experiment. Enter a whole number.

25

Random variable P is Normally distributed with mean 10 and standard deviation 3, and random variable Q is normally distributed with mean 9 and standard deviation 4. If P and Q are independent, which of the following describes the distribution of Q - P?

Normal with mean -1 and standard deviation 5

Events X and Y are independent, with P(X) = 0.6 and P(X and Y) = 0.18. Which of the following is true?

P(X or Y) = 0.72

As part of a demographic study, the SHS Equity Team needed to survey a sample of students from the school. From each grade level, the team randomly selected 10 percent of the students in each grade to participate in the survey. Which of the following is the best description of the type of sample selected by the Equity Team?

Stratified Random Sample

Based on the boxplot, which of the following statements is true?

The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.

Data will be collected on the following variables. Which variable can be considered discrete?

The number of books a person finished reading last month.

The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?

The proportion of the variation in height that is explained by a regression on age is 0.64

High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds. After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds. Let X represent the running time of a randomly selected student before training, and let Y represent the running time of the same student after training. Which of the following is true about the distribution of X−Y ?

The variables X and Y are not independent; therefore, the mean is 34 seconds and the standard deviation cannot be determined with the information given.

If two events are mutually exclusive, they cannot be independent

True