# Short Numericals on Probability, Range, Variability & Mean

1. Compute the arithmetic mean for the following data: 8, 2.2, 25, 7, -9, 10, 2, and 5.9.

2. An Embry-Riddle senior performed the same experiment on three groups of subjects

(with permission!) and obtained mean scores of 84, 69 and 76. The groups consisted of 13, 31, and 27 subjects respectively. What is the overall mean for all subjects?

3. For any distribution, the mean will have a z score equal to: ____________________.

4. A large set of sample scores yields a mean and standard deviation of 75.00 and 5.00 respectively. The distribution is roughly bell-shaped. What percentage of scores should fall between the values of 70.00 and 80.00?

5. Which grouping of scores exhibits the least variability?

2, 4, 6, 8, 10, 12

2, 3, 4, 10, 11, 12

6, 7, 7, 8, 12

2, 2, 3, 11, 12, 12

The variability is all the same.

6. Given two six sided dice, compute the probability of rolling a nine. Given two six sided dice, compute the probability of rolling two "11's" in a row.

7. A couple plans to have 4 children. Assuming the probability of obtaining each sex is 50% (1 in 2), find the probability of the couple getting four boys.

8. An election committee of three men and four women has been formed to elect a local representative. Each of the seven members must be assigned to investigate one of seven different candidates. How many different ways can those assignments be made?

9. Your state government decides to raise money by running a lottery where each ticket costs $1.00 and you must choose four different whole numbers between 1 and 20. When four numbers between 1 and 20 are randomly selected, what is the probability of winning if you have one ticket and the winning numbers can be in any order?

#### Solution Preview

QUESTIONS:

1. Compute the arithmetic mean for the following data: 8, 2.2, 25, 7, -9, 10, 2, and 5.9.

8

2.2

25

7

-9

10

2

509

Total 554.2

Mean= Total/n=554.2/8= 69.275

2. An Embry-Riddle senior performed the same experiment on three groups of subjects

(with permission!) and obtained mean scores of 84, 69 and 76. The groups consisted of

13, 31, and 27 subjects respectively. What is the overall mean for all subjects?

n Mean nX mean

13 84 1092

31 69 2139

27 76 2052

Total 71 5283

Mean= Grand Toatal/ N=5283/71= 74.41

3. For any distribution, the mean will have a z score equal to: ____________________.

z=(x-μ)/σ

where μ= Mean

σ= Standard deviation

4. ...

#### Solution Summary

The solutions provides answers to 9 questions on mean, standard deviation, range, probability, permutation.