Download NORMAL CURVE PROBLEMS

NORMAL CURVE PROBLEMS
1.
Suppose a variable X is normally distributed with a mean of 200 and a standard
deviation of 30. Calculate the probabilities below.
(a) P(180 ≤ X ≤ 215)
(c) P(X ≥ 180)
2.
(d) P(X ≥ 235)
What is the probability that a random car will lease for less than $200.00?
Find the probability that a random car will lease for more than $400.00?
What percentage of leases fall between $250.00 and $350.00 per month?
What is the cutoff cost for the most expensive 15% of the leases?
Grapefruits grown in a large orchard have a mean weight of 18.2 ounces with a
standard deviation of 1.2 ounces. Assuming that the weights of these grapefruits
are approximately normally distributed, what percentage of the grapefruits weigh:
(a) less than 16.1 ounces?
(c) between 16.7 and 18.8 ounces?
4.
(e) P(X ≤ 155)
A study of lease rates for a selection of 2007 compact cars revealed that the
average monthly rate for a vehicle was $270.67. The standard deviation was
$59.63. Assume the rates follow a normal distribution.
a.
b.
c.
d.
3.
(b) P(205 ≤ X ≤ 225)
(b) more than 17.3 ounces?
A “Car Buyer’s Guide” listed over 300 models of cars, with prices ranging from
under $10,000 to nearly $92,000. The average suggested retail price for these
cars was $28,454. The standard deviation was $13,875. Assume the data follow
a normal probability distribution.
a.
b.
c.
d.
e.
What is the probability a car costs less than $20,000?
What is the probability a car costs between $23,000 and the average price?
What is the probability a car costs between $25,000 and $35,000?
What is the probability a car costs at least $30,000 but less than $40,000?
Above what price are the most expensive 10% of the cars?
ANSWERS
1. (a) .4401
(b) .2292
(c) .7486
(d) .1210
2. (a) .1170
(b) .0150
(c) .5450
(d) $332.69
3. (a) .0401
(b) .7734
(c) .5859
4. (a) .2709
(b) .1517
(c) .2795
(d) .2529
(e) .0668
(e) $46,214.