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A small town hospitalhas historically one baby born every 2.0 days, onaverage. B

ID: 2955325 • Letter: A

Question

A small town hospitalhas historically one baby born every 2.0 days, onaverage.

Babies are bornunpredictably, at any time, and no birth is connected with anyother birth.

a. What is the probability thatat least 5 babies will be born at this hospital in thenext

week (7.0days)?

A local club providesa gift of a new car seat to the sixth baby born eachyear.

b. What are the expected value and standarddeviation of the time (in days) into next

year when the giftwill be awarded?

c. What is the probability that the gift will beawarded within 10 days of the

beginning of next year?

Explanation / Answer

1)

average 2 days per baby, then averagely 3.5 babies per week

P (5 babies in 7 days)

= e^(-3.5) * (3.5)^5 / (5!)

0.1322


2) Average days for sixth baby to be born = 6* 2 = 12 days

Standard deviation of baby born in 12 days period = (6)^0.5 = 2.45

Standard deviation of day for sixth baby = 2.45 / (6) * 12 = 4.9 days


3) Probability of the gift will be awarded in 10 days

= 1 - Probability of the gift will not be awarded in 10 days

= 1 - P(1 baby borned in 10 days) - P(2 baby borned in 10 days) - P(3 baby borned in 10 days) - P(4 baby borned in 10 days) - P(5 baby borned in 10 days)

= 1 - 0.60922

= 0.3908

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