Question

The US Environmental Protection Agency reports the average fuel costs for various makes of
cars. In recent years the fuel costs for mid‐size Japanese cars averaged $1200. Suppose that the
annual fuel costs for various makes of automobiles are normally distributed and that the
standard deviation of annual fuel costs for the mid‐size Japanese cars is $200. A mid‐size car
from the specified year is randomly selected from those that were sold. Answer the questions
below. It is strongly recommended that you do a sketch in each case to show the area(s) or
probability you are evaluating.

25. What is the probability that the annual fuel cost for a randomly selected car is greater
than $1000?
(a) 0.9323
(b) 0.8255
(c) 0.3413
(d) 0.8413
(e) 0.2823
26. What is the probability that the annual fuel cost is less than $1050?
(a) 0.2946
(b) 0.2734
(c) 0.7734
(d) 0.2266
(e) 0.0823
27. What is the probability that the annual fuel cost is between $1100 and $1350?
(a) 0.4322
(b) 0.1915
(c) 0.2417
(d) 0.6247
(e) 0.4649
28. What is the probability that the annual fuel cost is $1500 or less?
(a) 0.7088
(b) 0.4332
(c) 0.0668
(d) 0.8332
(e) 0.9332
29. What is the probability that the annual fuel cost is $1250 or more?
(a) 0.0987
(b) 0.4013
(c) 0.9010
(d) 0.9013
(e) 0.5261
30. What is the probability that the annual fuel cost is between $1225and $1275?
(a) 0.0908
(b) 0.0517
(c) 0.1480
(d) 0.0963
(e) 0.4261
31. Suppose that the standard deviation of the fuel cost is unknown. If 80% of all mid‐size
cars of that year had an annual fuel cost greater than $1030, what would be the value of
standard deviation if the mean fuel cost is $1200?
(a) 231.70
(b) 200.00
(c) 202.38
(d) 230.00
(e) 235.09
32. Suppose that the average annual fuel cost is unknown. What is the value of the mean
annual fuel cost for the mid‐size cars if 30.5% of the annual fuel costs are less than $1100
when the standard deviation is $200.
(a) 1100.70
(b) 1205.00
(c) 1202.00
(d) 1788.00
(e) 1235.09

Answer 1

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