Random Variables and Distributions

Binomial or Not Binomial?

Rolling a dice ten times and recording how many threes are rolled

• Binomial

• Not Binomial

In a preliminary audition, 40% of the candidates qualified for the finals of a singing competition.
If a sample of 12 candidates is selected at random, find the probability that 8 candidates from the sample qualified for the finals. Which are the correct mathematic statement for the case above?

Choose the correct sign

'probability between 4 and 9'

• P(4<X<9)

• P(4<X≤9)

• P(4≤X≤9)

• P(4≤X<9)

At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds.  Find the probability that out of the next eight eastbound cars that arrive randomly at the light,exactly three will be stopped by a red light.

• 0.254

• 0.147

• 0.027

• 0.1940

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy a magazine and thinks that he might be able to use the display space to sell something more profitable. What is the probability that at least 5 of his first 50 customers buy magazines?

• 0.104

• 0.896

• 0.066

• 0.774

What does the n stand for in the binomial probability formula?

• Number of trials

• Number of Successes

• Probability of Successes

• Probability of Failures

What does the p stand for in the binomial probability formula?

• Number of trials

• Number of Successes

• Probability of Successes

• Probability of Failures

Time to finish a race

• DISCRETE RANDOM VARIABLES

• CONTINUOUS RANDOM VARIABLES

Determine which of the following distribution is NOT a probability distribution. (Remember that a valid probability distribution must add up to 1)

• A

• B

• C

• D

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household? HINT: A Probability table may be helpful.

• 2.00

• 2.13

• 1.97

• 1.27