Data Driven Statistics

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.

(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.