The mean graduation time is 5 years with a standard deviation of 6 months for the Monte Carlo College, in which the graduation time is related to the grade of the students. The class size is normally 40. Calculate how many students may graduate by the end of the fourth year. Please show work.
To calculate the number of students who may graduate by the end of the fourth year, you need to determine the probability of a student graduating within four years and then multiply it by the class size.
Given that the mean graduation time is 5 years and the standard deviation is 6 months, we can calculate the graduation percentage within four years as follows:
First, convert the 5-year mean into months. Since there are 12 months in a year, the mean graduation time is 5 * 12 = 60 months.
Next, we need to find the z-score for four years (48 months). The formula for calculating the z-score is:
z = (x - μ) / σ
where:
x = value (in this case, 48 months)
μ = mean (in this case, 60 months)
σ = standard deviation (6 months)
Substituting the values into the formula, we get:
z = (48 - 60) / 6 = -12 / 6 = -2
Using a z-score table or calculator, we find that the corresponding cumulative probability for a z-score of -2 is approximately 0.0228. This means there is a 0.0228 probability of a student graduating within four years.
Finally, to calculate the number of students expected to graduate within four years, we multiply the probability by the class size:
Number of students = Probability * Class size
= 0.0228 * 40
= 0.912
Therefore, approximately 0.912 or 1 student is expected to graduate by the end of the fourth year based on the given data.