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Problem Solutions
1)
A friend of mine is pregnant.
It is known that birth weights of babies in the US are
approximately normally distributed with a mean of 3300 grams and a standard deviation of 375g
[http://en.wikipedia.org/wiki/Birth_weight].
a) Babies that weigh less than 2500 grams are often put into intensive care units.
What is the
probability she has a baby that will be administered to the intensive care unit?
b) What weight does her baby have to be in order to be in the heaviest 10% of all babies?
2)
The daily high temperature for the first week in October in Boston is approximately Normally
distributed with an average high of 66°F and a standard deviation of 7°F.
a) Yesterday, the high temperature was 57.8°F.
What is the probability that a day in the first week
of October would have a high of 57.8°F or colder?
b) What high temperature needs to be achieved in order to be in the top 1% of daily high temps in
the first week of October?
c) On the first day of October it got up to 83°F.
What is the probability that a day in the first
week of October would have a high of 83°F or warmer?
3)
The annual winter snowfall in Boston has an average of 43 inches and a standard deviation of
21 inches.
a) Let X be the random variable for the amount of snowfall Boston will get in a random winter.
Do you believe X will be normally distributed?
Could be…
b) To date, Boston has received 68 inches of snow this winter.
What is the probability that a
winter season will have at least 68 inches of snow (assuming a normal distribution)?
c) How much snow is needed to be in the top 1% of years in the amount of snowfall in Boston
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.
 Fall '11
 MichaelParzen
 Standard Deviation

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