Solve the following problems: In the table below, the random variable x represen
ID: 3160551 • Letter: S
Question
Solve the following problems:
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 (are) not satisfied.
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.
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.
x P(X) 0 0.22 1 0.16 2 0.21 3 0.16Explanation / Answer
1.
The data does not represent a probability distribution, because the probabilities do not sum up to 1.
[0.22 + 0.16 + 0.21 + 0.16 = 0.75 =/= 1]
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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.
Hence, the probability of getting a correct anwer is p = 1/5 = 0.2.
n = 100 here.
Hence,
u = mean = np = 20 [ANSWER]
s = standard deviation = sqrt(np(1-p)) = 4 [ANSWER]
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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.
Here, n = 100, p = 0.24.
Hence,
u = mean = np = 24 [ANSWER]
s = standard deviation = sqrt(np(1-p)) = 4.270831301 [ANSWER]
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