Question

The distribution of waiting times at the student health center is bell-shaped with a mean pf 12 minutes and a standard deviation of 3. What interval is likely to contain about 95% of wait times ?

a) [6,18] minutes
b) [9,15] minutes
c) [10,14] minutes
d) [3,21] minutes

Answer 1

The interval likely to contain about 95% of wait times at the student health center, which has a mean of 12 minutes and a standard deviation of 3 minutes, is calculated using the empirical rule to be [6,18] minutes. This corresponds to option (a).

Step-by-step explanation:

The question deals with the distribution of waiting times at a student health center, which is described as being bell-shaped (normally distributed). To find the interval that is likely to contain about 95% of wait times, we can apply the empirical rule, which states that approximately 95% of the data for a normal distribution lies within two standard deviations from the mean.

Given a mean (μ) of 12 minutes and a standard deviation (σ) of 3 minutes:

• The interval's lower bound is μ - 2σ = 12 - 2(3) = 6 minutes.
• The interval's upper bound is μ + 2σ = 12 + 2(3) = 18 minutes.

Therefore, the interval likely to contain about 95% of wait times is [6,18] minutes, which corresponds to option (a).