Binomial and Geometric

If a coin is flipped, what is the probability that the first head appears on the fifth flip?

Determine whether the given random variable has a binomial distribution, geometric distribution, or neither.

About one percent of the population is ambidextrous.  Suppose a polling company randomly contacts 50 people to ask if they are ambidextrous.  Let X = the number of people who are ambidextrous.

• Binomial

• Geometric

• Neither

Determine whether the given random variable has a binomial distribution, geometric distribution, or neither.

A state agency wishes to know if cars using the HOV (high-occupancy) lane have three or more occupants.  Let X = the numbers of cars that pass by until you see a car with three or more occupants.

• Binomial

• Geometric

• Neither

An online poll reported that 44% of respondents subscribe to the “five-second rule.” That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within five seconds. Let’s assume this figure is accurate for the entire U.S. population, and we select 15 people at random from this population. What is the expected number of people who subscribe to the five-second rule out of the 15 selected people?

• 5 people

• 6.6 people

• 7 people

• 4.4 people

According to a poll, 63.4% of people wash their hands after using a public restroom. Suppose a random sample of 20 people is taken. What is the probability that exactly 18 people washed their hands?

• 0.90

• 0.0070

• 0.023

• 0.999

A study found that 44% of people wash their hands before preparing food. Suppose a random sample of 30 people is selected. What is the probability that less than 10 people wash their hands before preparing food?

• 0.075

• 0.046

• 0.160

• 0.085

According to a National Geographic survey, 43% of adults can identify Ohio on an unlabeled map.  What is the probability that you must sample exactly 5 adults to find the first one who can identify Ohio on an unlabeled map?

• 0.045

• 0.43

• 0.034

• 0.086

According to a 2022 poll, 62% of high school graduates go to college. What is the probability that you must sample at least 3 high school graduates to find one who is going to college?

• 0.090

• 0.945

• 0.144

• 0.856

According to a 2018 poll, 24% of people carry lucky charms. Let’s assume this figure is accurate for the entire U.S. population, and we select 30 people at random from this population. Find and interpret the mean for the number of people in the sample who carry a lucky charm.

• We expect 7.2 people to carry lucky charms.

• We expect a randomly selected person to carry 7.2 lucky charms.

• If many, many samples of 30 people were selected, we would expect an average of 7.2 people to carry lucky charms.

• If many, many people were selected, we would expect an average of 7.2 lucky charms.