2. A competitor claims that its mid size car gets better
mileage than automakers new mid size model. The automaker used
sample information in a probability based on normal distribution to
provide strong evidence that the competitors claim is false.
3. Total Population 10000 Sample selected 49 of company Y
According to EPA (environmental protection agency) standards The
mean = 31.55 Standard Deviation = 0.7
4. Well use the normal probability distribution to prove that
the competitors claim is false. Secondary data will be used. Sample
of 49 mileages has been collected from company Y cars. Mean of
sample mileage =31.5 miles/gallon Standard deviation = 1.5
miles/gallon
5. Competing company = 33 = 0.7 Suppose that the competitor is
true in his argument P(32 x 35)
6. As it was supposed that the claim is true we therefore take
the values to be 32 and 35 instead of 32.3 and 33.7
7. P(32 x 35) = P P(32 x 35) = P(-1.43 z 2.86) From z
table(-1.42=.4236) & (2.86=.4979) P(32 x 35)=P
.4236+.4979=.9215x100=92.15% This probability says that if the
competing automaker claim is valid then 92.15% of all its midsize
cars will get mileages between 32mpg and 35mpg
11. The antipollution department and tax department agreed upon
Automakers producing cars with mileage of 31.5mpg will be tax-free
This will reduce pollution Will be more economical Customers will
be attracted to buy it
12. Suppose that an independent testing agency randomly selects
one of these cars and finds that it gets mileage of 31.2 mpg when
tested. Claimed mean = 33 Standard Deviation =0.7 Which contradicts
with the randomly selected car According to the claimed mean and
standard deviation the manufacturer should be declared tax-free.
Itll be proved that the manufacturers claim is false
13. To calculate the mileage x of a randomly selected car which
will be equal to or less than 31.2mpg p( x 31.2) The area under the
normal curve to the left side of 31.2 with mean 33.0 and standard
deviation 0.7 z= = = -2.57 Which shows that the mileage 31.2 is
2.57 standard deviation below the mean mileage = 33
15. It is very hard to believe that 51 cars out of 10000 will
have mileage below 31.2 Conclusion: We have a very strong evidence
against the competing automakers claim to be false. Reasons could
be: Mean is smaller than 33 Standard deviation is greater than 0.7
The population is not normally distributed