For the random variables below, indicate whether you would expect the distributi

Question

For the random variables below, indicate whether you would expect the distribution to be best described as geometric, binomial, Poisson, exponential, uniform, or normal. We do not have data, so you will not to use the computer for these questions. For each item, give a brief explanation of your answer. A one-sentence explanation should be sufficient.

The number of heads in 13 tosses of a coin.

The number of at-bats (attempts) required for a baseball player to get his first hit.

The height of a randomly chosen adult female.

The time of day (on Earth) that a solar flare occurs.

The number of automobile accidents in a town in one week.

The amount of time before the first score in a lacrosse game.

The number of times a die needs to be rolled before a 3 appears.

The number of particles emitted by a radioactive substance in five seconds.

Explanation / Answer

1. The number of heads in 13 tosses of a coin.

There are two possible outcomes: Head (Success) and tails (Failure). Trails are independent and probability of success is same in each trail. So this will be a binomial distribution.

2. The number of at-bats (attempts) required for a baseball player to get his first hit.

This is talking about the x number of trials before the first hit obtained so this will be geometric distribution.

3. The height of a randomly chosen adult female.

A continuous variable which will follow a normal distribution.

4. The time of day (on Earth) that a solar flare occurs.

This solar flare can occur anytime in a day so it is equally likely for all parts of the day and hence this will be uniform distribution.

5. The number of automobile accidents in a town in one week.

Here n is very large and probability of success (Accident occurs) is very small so this will follow Poisson distribution.

6. The amount of time before the first score in a lacrosse game.

Here it is related to the amount of waiting time before the first score so this will be an exponential distribution.

7. The number of times a die needs to be rolled before a 3 appears.

This will be the geometric distribution because it is about number of trials before first success appears.

8. The number of particles emitted by a radioactive substance in five seconds.

This will follow a Poisson distribution.

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