Solutions
Colour Preferences:
Black- 18
Red- 15
White- 9
Blue- – 8
Green-6
a. Point estimate of black colored cars: 18/56 = 9/28
b. The sampling distribution of the proportion of black cars, when the population proportion of
black cars is p=0.36 is:
p^ ~ Bin( p, p(1-p)/n), where n is the size of the sample.
p^ ~ Bin( .36, 0.0041)
c. For large n and p=0.36, the sampling distribution can be approximated by Normal distribution
P(.31<P<.41)
P((.31-.36)/sqrt(.0041)<Z< (.41-.36)/sqrt(.0041))
P(-.78<z<.78)
.7823- .2177= 0.5646 ( From Standard normal table).