1. A school approaches fire drills in the following way. At the start of each in
ID: 3364884 • Letter: 1
Question
1. A school approaches fire drills in the following way. At the start of each independent day, it randomly decides if there will be a fire drill, or not, in such a way that the probability of a fire drill on any individual day is .04.
a. What is the probability the first drill of the year occurs before the 20th day of the school year?
b. What is the probability the first drill occurs after the expected data for the first fire drill?
c. What is the probability the first happens between the 30th and 60th day of the year, inclusive?
2. Suppose that the amount of time you must wait outside MP building to catch your bus is uniformly distributed with a maximum of 20 minutes. What is the probability that you wait at least 12 minutes of your bus?
Explanation / Answer
a)probability the first drill of the year occurs before the 20th day of the school year=1-P(till 19th day no fire drill)
=1-(0.96)19 =0.5396
b)expected date for first drill =1/0.04 =25
probability the first drill occurs after the expected data for the first fire drill =P(no drill till 25st day) =(0.96)25 =0.3604
c)
probability the first happens between the 30th and 60th day of the year, inclusive
=
P(till 29 day no fire drill)*P(at least one drill in next 31 days) =(0.96)29*(1-(0.96)31) =0.2197
2) probability that you wait at least 12 minutes of your bus =P(X>12) =(20-12)/20 =8/20=0.4
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