Final answer:
The variable of interest is the number of students enrolled in CPR classes. This variable is discrete. The probability distribution table meets the criteria of having probabilities between 0 and 1, and the sum of all probabilities equals 1. To find the mean enrollment, you multiply each enrollment by its respective probability, and sum these values. To find the standard deviation, you calculate the squared difference between each enrollment and the mean, multiply it by its probability, and sum these products.
Step-by-step explanation:
The variable of interest in this question is the number of students enrolled in CPR classes offered by the local fire department.
This variable is discrete, as it can only take on whole number values.
The criteria met to make this table a probability distribution table include:
- All probabilities are between 0 and 1.
- The sum of all probabilities is equal to 1.
To find the probability that at least 15 students will enroll in the CPR class, you would sum the probabilities of 15, 16, 17, and so on, up to the maximum number of students.
The mean enrollment for CPR classes can be found using the formula:
Mean = ∑(x * P(x))
where x represents each possible enrollment and P(x) represents the probability of that enrollment. You would calculate the product of each enrollment and its probability, and then sum all of these products to find the mean enrollment.
To compute the standard deviation of the probability distribution, you would use the formula:
Standard Deviation = sqrt(∑((x - Mean)^2 * P(x)))
where x represents each possible enrollment, Mean represents the mean enrollment, and P(x) represents the probability of that enrollment. You would calculate the squared difference between each enrollment and the mean, multiply it by its probability, and then sum all of these products. Finally, you would take the square root of the sum to find the standard deviation.