Perez Statistic Exercise 1

1. In the table below, the random variable x represents the number of cups or cans of caffeinated beverages consumed by Americans each day, based on data from the National Sleep Foundation.
Determine whether or not the data represent a probability distribution.
*If the data represent a probability distribution, find its mean and standard deviation.
* If the data don’t represent a probability distribution, identify the requirement(s) for a probability distribution that is not satisfied.

The data does not represent a probability distribution because all the probabilities are between 0 and 1 but the sum of the probabilities does not equal 1.
0.22+ 0.16+ 0.21 + 0.16 = 0.75 therefore, this is not a probability distribution since the sum of the P(x)'s is not 1

2. The final exam in a sociology course consists of 100 multiple-choice questions. Each question has five possible answers, and only one of them is correct. An unprepared student makes random guesses for all the answers. Find the mean and standard deviations for the number of correct answers for this student

Mean = n (p)
Standard deviation =

q = 1- p (1 - .2 = .8) n = 100 p = 1/5 (.2)

(Mean) = 100) = 20

Standard deviation = = = 4

The mean for the number of correct answers for this student is 20.

The standard deviation for the number of correct answers for this student is 4.
3. Mars, Inc. claims that 24% of its M&M plain candies are blue. A sample of 100 M&Ms is randomly selected. Find the mean and standard deviations for the number of blue M&Ms in such a group of randomly selected 100 candies

Mean = n (p)
Standard deviation =

q = 1- p (1 - .24 = .76) n = 100 p = .24

(Mean) = 100) = 24

Standard deviation = = = 4.27

The mean for the number of blue M&Ms in such a group of randomly selected 100 candies is 24.

The standard deviation for the number of blue M&Ms in such a group of randomly selected 100 candies is 4.27