Exam 8: Random Variables

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 time of x =30 seconds?

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 probability that exactly 3 children will have blue eyes?

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 interquartile range for waiting time?

Suppose that in a large population, the proportion that is left-handed is p = 0.10. Suppose n = 20 people will be randomly selected and X = number of people in the sample who are left-handed. What probability model should be used to find the probability that X = 3?

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 standard deviation for the number of men in a sample of 120 teachers?

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -What is the probability that a randomly chosen student will take at least an hour to complete the exam?

Use the following information for questions: The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes. -By what time should 67% of the students have finished the exam? (i.e. What is the 67^th percentile for X?)

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 probability that all 4 children will have blue eyes?

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 -How many men would we expect to find in the sample of 120 teachers?

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 variance for the number of children with blue eyes, V(X)?

Use the following information for questions: The Southside Bowling Alley has collected data on the number of children that come to birthday parties held at the bowling alley. Let the random variable X = the number of children per party. The distribution for the random variable X is given below. -Suppose one party is to be randomly selected. What is the expected number of children that will attend this party? Include the appropriate symbol and units in your answer.

Use the following information for questions: Based on her past experience, a professor knows that the probability distribution for X = number of students who come to her office hours on Wednesday is given below. -What is the value of the cumulative probability distribution at 2, i.e. P(X $\le$ 2)?

Pulse rates of adult men are approximately normal with a mean of 70 and a standard deviation of 8. Which choice correctly describes how to find the proportion of men that have a pulse rate greater than 78?

Use the following information for questions: The time it takes a student to finish buying his/her text books, W, is a normal random variable. This variable W is the sum of two other normal variables, X and Y (W = X + Y), where X = the time to wait in line at the ATM machine to get cash, and Y = the time to wait in line at the cashier to buy the books. Assume that X and Y are independent normal random variables, with the following means and standard deviations: -What is the expected time it takes a student to finish buying his/her text books?

Use the following information for questions: Based on her past experience, a professor knows that the probability distribution for X = number of students who come to her office hours on Wednesday is given below. -What is the probability that at least 2 students come to office hours on Wednesday?