In a certain Math class, the probabilities have been empirically determined for various numbers of
absentees on any given day. These values are shown in the table below. Find the expected number of
absentees in a given day.
Number of
absentees, x
0 1 2 3 4
Probability,
P(x)
0.18 0.26 0.29 0.23 0.04
11
Well, it seems like the number of absentees is really taking attendance seriously, or should I say "absenting" seriously. Anyway, let's get down to business.
To find the expected number of absentees in a given day, we'll have to use a little bit of math. We can calculate it by multiplying each number of absentees (x) by its corresponding probability (P(x)), and then add up all the products.
Let's do the math:
Expected number of absentees = (0 * 0.18) + (1 * 0.26) + (2 * 0.29) + (3 * 0.23) + (4 * 0.04)
Now let's calculate:
Expected number of absentees = 0 + 0.26 + 0.58 + 0.69 + 0.16
Expected number of absentees = 1.69
So, the expected number of absentees in a given day is 1.69. Just remember, though, that this is an expected value and not an absolute guarantee. Absentees can be a funny bunch sometimes!
I hope that answers your question!
To find the expected number of absentees in a given day, you can use the formula for expected value. The expected value is calculated by multiplying each possible outcome by its probability, and then summing up these products.
In this case, you can calculate the expected number of absentees as:
E(X) = (0 * 0.18) + (1 * 0.26) + (2 * 0.29) + (3 * 0.23) + (4 * 0.04)
Now, let's calculate this value step-by-step:
E(X) = (0 * 0.18) + (1 * 0.26) + (2 * 0.29) + (3 * 0.23) + (4 * 0.04)
= 0 + 0.26 + 0.58 + 0.69 + 0.16
= 1.69
Therefore, the expected number of absentees in a given day is 1.69.
To find the expected number of absentees in a given day, you need to multiply the number of absentees (x) by their respective probabilities (P(x)), and then sum up the products.
In this case, you have the following data:
Number of absentees, x: 0, 1, 2, 3, 4
Probability, P(x): 0.18, 0.26, 0.29, 0.23, 0.04
To calculate the expected number of absentees, you can use the formula:
Expected value = x1 * P(x1) + x2 * P(x2) + x3 * P(x3) + ... + xn * P(xn)
where xi represents each number of absentees, and Pi represents their respective probabilities.
Let's calculate it step by step:
Expected value = (0 * 0.18) + (1 * 0.26) + (2 * 0.29) + (3 * 0.23) + (4 * 0.04)
Expected value = 0 + 0.26 + 0.58 + 0.69 + 0.16
Expected value = 1.69
Therefore, the expected number of absentees in a given day is 1.69.