Question

Let us suppose that the time from Simon getting out of bed until his arrival at school is normally distributed with a mean of 55 minutes and a standard deviation of 5 minutes. Simon's arrival at school is classified as being late if it occurs after 9.10 am.

a. One day Simon gets out of bed at 8.08 am. What is the probability of him arriving late?
b. For a period of time Simon always gets out of bed at the same time but finds that he arrives late approximately 85% of the time! What time is he getting out of bed (to the nearest minute)?

Answer 1

The student's questions about Simon's probability of arriving late and what time he should get out of bed given an 85% late rate are solved using Z-scores and the properties of the normal distribution.

Step-by-step explanation:

The question covers the concept of normal distribution in probability, which is applicable to various real-world scenarios, including a student's morning routine to get to school. The problem has two parts:

1. Determining the probability of Simon arriving late at school if he gets out of bed at 8.08 am.
2. Figuring out the time Simon should get out of bed to minimize his chances of being late, given a 85% late arrival rate.

To solve part a, we need to calculate the Z-score for Simon arriving at 9.10 am, assuming he got out of bed at 8.08 am. From the Z-score, we can find the corresponding probability of Simon being late. Part b requires using the Z-score that corresponds to the 85th percentile of a normal distribution and working backward to find the time Simon gets out of bed.