Exam 8: Random Variables

Use the following information for questions: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. -Random variable X = the number of letters in the last name of a student picked at random from a class on English composition.

Which of the following is an example of a binomial random variable?

Suppose that vehicle speeds at an interstate location have a normal distribution with a mean equal to 70 mph and standard deviation equal to 8 mph. What is the z-score for a speed of 64 mph?

Use the following information for questions: Midterm Exam Results reported as z-scores. -Greg is in another section of the course. The distribution of midterm scores for his section was reported as being approximately normal with a mean of 62 and a standard deviation of 8. Greg's standardized score is +1. What is Greg's midterm score?

Scores on an achievement test had an average of 70 and a standard deviation of 10. Serena's score was 85. Assuming the scores have approximately a normal distribution, about what proportion of students scored lower than Serena?

Use the following information for questions: In a family with 4 children, the number of children with blue eyes is a binomial random variable X with n = 4 and p = .20. -What is the expected number of children with blue eyes, E(X)?

Weights of females have approximately a normal distribution with mean 135 lbs. and standard deviation 20 lbs. Allison weighs 145 lbs. What is the z-score for her weight?

The time taken to answer an exam question for a randomly chosen student has a uniform probability distribution from 1 minute to 5 minutes. What is the probability that the time to answer is no more than 2 minutes?

Assuming a standard normal distribution is appropriate, what is the approximate probability that a z-score is greater than or equal to 2.33? Said another way, what is P(Z $\geq$ 2.33)?

Use the following information for questions: The time to complete an exam for a randomly chosen student in a textiles class is a normal random variable with a mean of 50 minutes and a standard deviation of 10 minutes. -At what time will 75% of the class have finished the exam? (i.e. What is the 75^th percentile of the distribution?)

Use the following information for questions: A child is observing squirrels in the park and notices that some are black and some are gray. For the next five squirrels she sees, she counts X = the number of black squirrels. Suppose X is a binomial random variable with n = 5 and p = 0.50. -What is the probability that she will see exactly one black squirrel out of the five?

Use the following information for questions: Suppose X is a binomial random variable with n = 800 and p = 0.20. -Find the expected value E(X).

Use the following information for questions: The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. -What is the standardized score (z-score) for a boot-up of time x =35 seconds?

Use the following information for questions: Joan has noticed that the probability distribution for X = number of students in line to use the campus ATM machine when she shows up to use it is shown below. -The variance of X, V(X) = 1.16. What is the standard deviation of X?

Use the following information for questions: Suppose the time to wait for placing an order at a drive-through window has a uniform distribution between 0 and 8 minutes. -What is the expected waiting time?

Use the following information for questions: According to the National Education Association, the country's largest teachers union, the proportion of men in teaching is at its lowest level in 40 years. Only 21 percent of teachers in U.S. public schools are men. In early grades, the gender ratio is even more imbalanced - just 9 percent of elementary school teachers are men. Suppose we randomly select 120 teachers who work in U.S. public schools -What is the (approximate) probability that less than 20 of these teachers are men?

Use the following information for questions: A child is observing squirrels in the park and notices that some are black and some are gray. For the next five squirrels she sees, she counts X = the number of black squirrels. Suppose X is a binomial random variable with n = 5 and p = 0.50. -What is the expected number of black squirrels she will see, E(X)?

Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the will student get 8 or fewer answers correct?

Use the following information for questions: Ellen is taking 4 courses for the semester. She believes that the probability distribution function for X = the number of courses for which she will get an A grade is given below. -What is the standard deviation for the number of A's she will get?

Use the following information for questions: Ellen is taking 4 courses for the semester. She believes that the probability distribution function for X = the number of courses for which she will get an A grade is given below. -What is the expected number of A's she will get? (i.e. What is E(X)?)