# Data Driven Statistics

**Question description**

1. A company gave psychological test to prospective employees. The random variable x represents the possible test scores. The test scores are as follows.

0 0.06

1 0.27

2 0.33

3 0.24

4 0.10

Find
the probability that a person selected at random from the surveys sample test
score of more than two. **(ROUND TO TWO DECIMAL PLACES AS NEEDED)**

2. A frequency distribution is shown below. Complete parts a through d.

The number of dogs per household in a small town.

Dogs |
Households |

0 |
1460 |

1 |
402 |

2 |
164 |

3 |
46 |

4 |
25 |

5 |
12 |

**(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.)**

**(b) **Find
the mean of the probability distribution.

**(c) **Find
the variance of the probability distribution.

**(d) **Find
the standard deviation of the probability distribution.

**3. **47% of men consider themselves professional
baseball fans. You randomly select 10
men and ask each if he considers himself a professional baseball fans. Find the probability that the number who
considers themselves baseball fans is (a) exactly eight, (b) at least eight,
and (c) less than eight. (c) Less than
eight. If convenient, use technology to
find the probabilities.

**4. **5% of
people in a city eligible to donate blood actually do. You randomly select four eligible blood
donors and ask them if they donate blood.

**X P(x)**

0 .845

1 .171

2 .014

3 .000

4 .000

The binomial distribution for n =4 and p=0.05 is shown above.

Interpret the results in the context of the real life situation. What values of the random variable x would use consider unusual?

On average, ___ eligible adults out
of every 4 give blood. The standard
deviation is ___, so most samples of four eligible adults would differ from the
mean by at most ___ adult(s). The
value(s) **X =2, X = 3, X=4 , or x=0, and
x=1, or x=0 **would be unusual because of their probabilities are **equal to, more than, or less than **0.05

**(ROUND TO FOUR DECIMAL PLACES AS NEEDED)**

**5. **Find
the area of the indicated region under the standard normal curve.

The area between z=0 and z=1.1 the standard normal curve is ___.

(On the graph not shown the z is on the right if this helps.)

**(ROUND
TO FOUR DECIMAL PLACES AS NEEDED)**

6. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age groups, the heights were normally distributed, with a mean of 68.3 inches and standard deviation of 3.0 inches. A study participant is randomly selected.

Find the probability that is less than 65 inches.

Ans: z =(65 – 68.3)/3 = -1.1

P(x < 65) = P(z < -1.1) = **0.1357**

The probability that the study participant selected at random is less than
65 inches tall is ___**0.1357**

**PART B.
Find the Find the probability that his height is between 65 and 71
inches.**

The probability that the study participant
selected at random is between 65 and 71 inches tall is ___** (ROUND TO FOUR DECIMAL PLACES AS NEEDED.)**

7. Find the indicated z- score.

The area on the graph that is shaded is 0.3745

**(ROUND
TO TWO DECIMAL PLACES AS NEEDED)**

The z-score is ___

8. Find the z-score that has 10.2% of the distributions area to its right.

The z-score is ___

**ROUND
TO TWO DECIMAL PLACES AS NEEDED)**

**2. **In
a survey of women is a certain country (ages 20-29), the mean height was 65.6
inches with a standard deviation of 2.82 inches. Answer the following questions about the
specified normal distribution.

**(a) **What
height represents the 98^{th} percentile?

**(b) **What
height represents the first quartile?

**(ROUND TO TWO DECIMAL PLACES AS
NEEDED)**

**9. **The
time spent in days waiting for a heart transplant in two states for patients
with type A+ blood can be approximated by normal distribution, as shown in the
graph.

(a) What is the shortest time spent waiting for a heart that would still place a patient in the top 5% of waiting. ___ Days.

(b) What is the longest time spent waiting for a heart would still place a patient is the bottom 15% of waiting time. ___days

**(ROUND
TO TWO DECIMAL PLACES AS NEEDED.)**

**For question 7.**

**For question 9**.

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