Exam 8: Random Variables

Use the following information for questions: Midterm Exam Results reported as z-scores. -The professor for one section of a multi-section math course will be reporting his students' midterm exam scores as z-scores. Jackson's score on the midterm exam was 82 points. The section's class mean was 75 and the standard deviation was 5 points. What was his z-score?

The payoff (X) for a lottery game has the following probability distribution. What is the expected payoff?

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 a word picked at random out of the dictionary.

The number of first-year students who will decide to live in dormitories is a binomial random variable X with n = 1000 and p = 0.50. Use the normal approximation with continuity correction to approximate the probability that X will be no more than 490, P(X $\leq$ 490).

The mean for a population of N values is equivalent to

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 1 student comes to office hours on Wednesday?

Use the following information for questions: Midterm Exam Results reported as z-scores. -Continuation of 105. What percentile does Greg's score correspond to?

Which one of these variables is a binomial random variable?

Verbal SAT scores have a mean of 500 and a standard deviation of 100. Which of the following describes how to find the proportion of Verbal SAT scores that are greater than 600?

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 =20 seconds?

Use the following information for questions: In an experiment, a person guesses which one of three different cards a researcher has randomly picked (and hidden from the person who guesses). This is repeated four times, replacing the cards each time. Let X = number of correct guesses in the four tries. The probability distribution for X, assuming the person is just guessing, is partially provided below. -What is the value of the missing probability P(X = 4)?

Which one of these variables is a continuous random variable?

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. -Complete the sentence: About 25% of the customers are expected to wait at most ____ minutes?

Which one of the following probabilities is a cumulative probability?

Use the following information for questions: Find the requested probability for the standard normal random variable Z. -What is the probability that Z is less than or equal to 2, P(Z $\leq$ 2)?

Use the following information for questions: In an experiment, a person guesses which one of three different cards a researcher has randomly picked (and hidden from the person who guesses). This is repeated four times, replacing the cards each time. Let X = number of correct guesses in the four tries. The probability distribution for X, assuming the person is just guessing, is partially provided below. -What is the probability that the person would get 3 or more correct guesses?

In a gambling game, on every play, there is a 0.1 probability that you win $7 and a 0.9 probability that you lose $1. What is the expected value of this game?

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. -What percent of the class will have finished the exam by 75 minutes?

What characteristic of a random variable is described by the expected value?

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. We know that there will be at least 7 children at this party. What is the probability that there will be 10 children at the party?