Random Variables and Probability Distributions

If we want to calculate the probability of rolling a 6 for the first time on the 6^th roll of a die, would we use the geometric or the binomial distribution?

• geometric

• binomial

When rolling a fair die 100 times, what is the probability of rolling a "4" exactly 25 times? Is this an example of binomial or geometric?

• binomial

• geometric

Which one of these variables is a continuous random variable?

• The time it takes a randomly selected student to complete an exam.
• The number of tattoos a randomly selected person has.
• The number of women taller than 68 inches in a random sample of 5 women. 
• The number of correct guesses on a multiple choice test. 

Which one of these variables is a discrete random variable?

• Time it takes a randomly selected student to complete a multiple choice exam.

• The heights of randomly selected students in the class.

• Distance between the students' home and school.

• Number of pairs of shoes a randomly selected person owns.

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

• Yes
• No, the trials are not independent.
• No, there are more than 2 outcomes

A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions.

What is the probability of getting exactly 6 questions correct on this test?

• (10C6)(1/5)⁶(4/5)⁴

• (10C5)(1/5)⁶(4/5)⁴

• (10C6)(1/5)⁶(4/5)⁵

• (10C5)(1/6)⁵(5/6)⁵

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?

• Find the probability that X=8 in a binomial distribution with n = 20 and p=0.5.

• Find the area between 0 and 8 in a uniform distribution that goes from 0 to 20.

• Find the probability that X=8 for a normal distribution with mean of 10 and standard deviation of √5

• Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14
• 4.67
• 5
• 7.5

A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries.

• 0.876

• 5

• 2.2304

• 0.9599

• The answer is not listed

When you add a positive constant to a random variable the effects on the random variables distribution are as follows:

• the shape is changed, the mean is increased by a value of "a" and the standard deviation is unchanged.

• the shape and standard deviation are unchanged and the mean is increased by a value of "a".

• all three aspects are unchanged

• the shape and mean are unchanged and the standard deviation is increased by a value of "a".