A grocery store receives its delivery each morning at a time that varies uniformly between 5 AM and 7 AM. On any given day, what is the probability that the time of delivery will be within 10 minutes of the expected time?

Expert Answers

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The grocery store receives its delivery each morning at a time that varies uniformly between 5 AM and 7 AM. This is a 7 - 5 = 2 hour period in which the delivery is made with the same probability.

2 hours is equal to 120 minutes which is equal to 12 intervals of 10 minutes each. The probability that the delivery is made in any particular 10 minute interval is 1/12

If delivery is within 10 minutes of the expected time on any day there is a 20 minute interval; 10 minutes before the expected time and 10 minutes after the expected time in which the delivery is made. The probability of this happening is 2*(1/12) = 1/6

There is a probability of 1/6 that the delivery is made within 10 minutes of the expected time.

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