Reference no: EM133153082
Bill Canry is the headmaster at Heller Highwater High School. It's a small rural public school with 9 teachers and 100 students. A snowstorm is bearing down on the region, and this has made it difficult to decide whether school should stay open tomorrow. State law requires 5 hours of instruction per day for it to count toward their required 175 days of class instruction. Classes start at 8:30 AM every day, and end at 3:00 PM.
If at least seven (7) teachers can make it to the school by 9:30 AM (= 1 hour late), the school can stay open and have a valid (state approved) instructional day. If fewer than seven teachers make it by 9:30 AM, it won't count as an instructional day, and Headmaster Canry should cancel school and call it a snow day.
Based on past data for snowy weather, arrival delays for each teacher follow a normal distribution adjusted for how far each teacher lives from the school (negative arrival delay values mean the teacher arrived before 8:30 AM). The mean and standard deviation for each of the nine teachers (in minutes) is given in the table below. (Notice that the standard deviation is twice the mean, which should help eliminate transcription errors).
|
Teacher
|
mean (min)
|
stan. dev. (min)
|
|
1
|
30
|
60
|
|
2
|
35
|
70
|
|
3
|
20
|
40
|
|
4
|
25
|
50
|
|
5
|
45
|
90
|
|
6
|
40
|
80
|
|
7
|
55
|
110
|
|
8
|
45
|
90
|
|
9
|
15
|
30
|
A. What is the probability that Heller Highwater High School can hold a valid instructional day?
B. If the headmaster's decision rule is to cancel school whenever the probability of a non-instructional day is greater than 1/3, what should he do?