According to a college survey, 71% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 33.
To find the standard deviation for the number of students who work full time in samples of size 33, we need some additional information. Specifically, we need to know the standard deviation of the population proportion (p), which represents the proportion of all college students who work full time.
Let's assume that the standard deviation of the population proportion (p) is known and denoted as σp. In this case, the standard deviation of the number of students who work full time in samples of size 33 (σ) can be calculated using the following formula:
σ = sqrt((p * (1 - p)) / n)
Where:
- σ represents the standard deviation of the sample
- p represents the population proportion (71% = 0.71 as a decimal)
- (1 - p) represents the complement of p (proportion of students who do not work full time)
- n represents the sample size (33 in this case)
By substituting the given values into the formula, we can calculate the standard deviation:
σ = sqrt((0.71 * (1 - 0.71)) / 33)
Calculating the expression inside the square root:
σ = sqrt((0.71 * 0.29) / 33)
Simplifying further:
σ = sqrt(0.2069 / 33)
Finally:
σ ≈ sqrt(0.00627)
Using a calculator or software, we can find the approximate value of the standard deviation:
σ ≈ 0.079 (rounded to three decimal places)
Therefore, the standard deviation for the number of students who work full time in samples of size 33 is approximately 0.079.