In an elementary school, 29% of children wear glasses. Suppose that a random sample of 31 children is selected. Find the mean number of children in the sample who wear glasses. Round your answer to the nearest integer.
36
To find the mean number of children in the sample who wear glasses, we can use the formula for the expected value of a binomial distribution.
The formula for the expected value of a binomial distribution is given by:
E(X) = n * p
Where:
E(X) is the expected value (mean) of the number of successes,
n is the number of trials (sample size), and
p is the probability of success (proportion of children who wear glasses).
In this case, we are given that the proportion of children who wear glasses is 29%, which can be written as 0.29. The sample size is 31 children.
Substituting the values into the formula:
E(X) = 31 * 0.29
Calculating the expected value:
E(X) = 8.99
Rounding the answer to the nearest integer:
E(X) ≈ 9
Therefore, the mean number of children in the sample who wear glasses is approximately 9.