Final answer:
To find the percentage of college graduates who take longer than 4 years to graduate, calculate the z-score for 48 months using the given mean and standard deviation. Look up this z-score in a standard normal distribution table to find the corresponding percentile, which represents students who graduate in less than 4 years. Thus, 84.1% of students graduate in more than 4 years.
Step-by-step explanation:
The question at hand involves calculating the percentage of college graduates who will take longer than 4 years (48 months) to graduate, assuming the time taken to graduate follows a normal distribution with a mean of 58 months and a standard deviation of 10 months. To find this, we will use the concept of z-scores in a normal distribution.
First, we calculate the z-score for 48 months: z = (X - μ) / σ, where X is 48 months, μ (mu) is the average number of months to graduate (58 months), and σ (sigma) is the standard deviation (10 months). Therefore, the z-score would be (48 - 58) / 10, which is -1.
Next, we look up the z-score of -1 on a standard normal distribution table or use a calculator that provides the cumulative probability. A z-score of -1 corresponds to the percentile approximately 15.9%. Since the distribution is symmetric, if 15.9% is below 48 months, then 84.1% is above it.
Therefore, the percentage of college graduates who take longer than 4 years to graduate would be 84.1%. The correct answer is C. 84.1%.