# Data Driven Statistics

**Question description**

1. What is a discrete probability distribution? What are the two conditions that determine a probability distribution?

What is a discrete probability
distribution? **Choose the correct answer below**.

(a.) A discrete probability distribution list each possible value a random variable can assume.

(b.)A discrete probability distribution lists each possible value a random variable can assume, together with its probability.

(c.) A discrete probability distribution exclusively lists probabilities.

(d.)None of the above.

2. Decide whether the random variable x is discrete or continuous. Explain you reasoning. Let x represent the temperature of a person taken with a mercury thermometer.

Is the random variable x discrete or continuous?
**Choose
the correct answer below.**

(a.) Continuous, because x is a random variable that cannot be counted.

(b.)Discrete, because x is a random variable that can be counted.

3. A frequency distribution is shown below. Complete parts (a) through (e).

The number of dogs per household in a small town

Dogs |
Households |

0 |
1477 |

1 |
428 |

2 |
170 |

3 |
41 |

4 |
27 |

5 |
15 |

(a) Use the frequency distribution to construct a probability distribution.

X P(x)

0 ___

1 ___

2 ___

3 ___

4 ___

5 ___

**(Round to the nearest thousandth
as needed)**

**4. ****The
expected value of an accountant’s profit and loss analysis is 0. Explain what this means.**

**Choose
the correct answer below.**

(a.) An expected value of 0 means that there was not any money gained or spent.

(b.)An expected value of 0 mans that the average money gained is equal to the average money spent, representing the break -even point.

(c.) Since the expected value cannot be less than 0, an expected value of 0 mans that the average money gained is equal to or less than the average money spent.

(d.)An expected value cannot be equal to 0.

5.
In a
binomial experiment, what does it mean to say that each trial is independent of
the other trials? **Choose the correct answer below.**

**(a.) **Each trial is independent of the other trials
if the outcome of one trial affects the outcome of another trial.

**(b.)**Each
trial is independent of the other trials if no more than one trial occurs at a
time.

**(c.) **Each
trial is independent of the other trials if the outcome of one trial does not
affect the outcome of any of the other trials.

**(d.)**Each
trial is independent of the other trials if the sum of all the possible trial
outcomes equals 1.

6. About 50% of babies born with a certain ailment recover fully. A hospital is caring for seven babies born with this aliment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Specify the value of n, Select the correct choice below and fill in answer boxes in your choice.

(a.) N =___

(b.)The answer is undefined.

7. Find the mean, variance and the standard of the binomial distribution with the given values of n and p.

N=70, p=0.6

**Round to the nearest tenth as needed.**

**8. **52%
of men consider themselves professional baseball fans. You randomly select 10
men and ask each if he considers himself a professional baseball fan. Find the probability that the number who
consider themselves baseball fans is (a)
exactly eight, (b) at least eight, and (c) less than eight. If convenient, use technology to find the
probabilities.

**(a.) ****P(8)
= ___ Round to the nearest thousandth as
needed.**

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