Name: ________________________________
Normal Distributions WS
AP Statistics
Answers are from calculator method – table method should be close
1) Professor Rogers has found that the grades on the nursing final exam are normally distributed with
a mean of 64 and standard deviation of 11.
a) If the passing grade is 54, what percent of the class will fail? .1816
b) If Professor Rogers wants only 85% of the class to pass, what should the passing grade be?
X = 52.60
2) The life of a coffee pot is approximately normally distributed with a mean of 5 years and standard
deviation of 1.1 years. The manufacturer will repair or replace any defective coffee pot free of
charge (including labor) while the pot is under warranty. For how many years should the company
guarantee its coffee pots, if the manufacturer does not wish to replace more than 5% of them?
X = 3.19 years
Hint: 5% in lower tail
3) A new filling machine has been installed on an assembly line that is supposed to fill each bag with 5
pounds (80 ounces) of sugar. However, the machine is not functioning properly and can be adjusted to
the vendor’s specifications. It is known that the filling process is approximately normally distributed
with a standard deviation of 2.4 ounces. At what level should the mean be set so that at most 5% of
the time will the bags contain more than 83 ounces of sugar?
 = 79.05 oz
4) The drying time of one particular paint is approximately normally distributed with a mean of 45
minutes. It is also known that 15% of walls painted with this paint need more than 55 minutes to
dry completely. Find the standard deviation of this distribution.
 = 9.648 minutes
5) The Fight For Life emergency helicopter service is available for medical emergencies occurring 15
to 90 miles from the hospital. A long-term study of the service shows that the response time from
receipt of the dispatch call to arrival at the scene of the emergency is normally
distributed with standard deviation of 8 minutes.
a) What is the mean response time (to the nearest whole minute) if only 6.7% of the calls require
more than 54 minutes to respond?  = 42.012 min
b) For a randomly received call, what is the probability that the response time will be less than
30 minutes? .067
c) For a randomly received call, what is the probability that the response time will be within 1.5
standard deviations of the mean? Hint: 42 ± 12
.8664
6) The American Veterinary Association claims that the annual cost of medical care for dogs averages
$100 with standard deviation of $30, and for cats, annual cost averages $120 with standard deviation
of $35. Assume that the annual veterinary expenses are independent and normally distributed.
Suppose you have a dog and a cat.
a) Describe the distribution of annual veterinary cost for your dog and cat. N($220,$46.0977)
b) What is the probability that your annual cost will be more than $250? .2576
c) What is the probability that your annual cost will be within $50 of the mean?
.7219