The School Bus?

Question

Bus arrival times at a school are normally distributed. The average arrival time is 8:00 AM. and the standard deviation is 5 minutes.

What is the probability that a bus will arrive between 7:55 AM and 8:10 AM? Explain.

Answer 1

I think Angel has the right idea, but the wrong implementation. (Or rather she DID, but she went back and fixed it.)

You'd expect the probability to be well over 50%, right?

From a normal distribution table, I see that the "z value" for 1 standard deviation is 0.3413, and for 2 standard deviations is 0.4772. (The z-value is the area under the curve between the mean and the standard deviation, in either direction.)

So, I think the actual answer should be: 0.3413 + 0.4772 = 0.8185, or 81.85% probability.

Or, using her method, correctly:

P(Z <= 2) - (1 - P(Z <=1))
0.9772 - (1 - 0.8413) = 0.8185, or 81.85%.

Answer 2

mean=8:00
standard deviation= 5 min

P(7:55<=x<=8:10)
=P((7:55-8:00)/5 <=(x-8:00)/5 <= (8:10-8:00)/5)
=P(-5/5 <=Z<=10/5)
=P(-1<=Z<=2)
=P(Z<=2)-(1-P(Z<=1))
=0.9773-(1-0.8413)
=0.9773-0.1587
=0.8186

notations:
<= : less than or equal to...
and i got the numbers from normal distribution table...

Answer 3

You could narrow this down to between 7:55 and 8:05 with a 100% probability, but not a given by any means. The unexpected could happen on any given day.

Answer 4

i think the probability could be decreased from 7:55 and 8:10 to 7:55and 8:05