Question

Of all the registered automobiles in Texas, 58% are sport utility vehicles. Suppose Carol’s neighborhood has 20 vehicles registered. What is the probability that a majority of them are sport utility vehicles.

Answer 1

Here we can model the vehicles as sport utility or not. Therefore it is an example of binomial model.

n = 20 p= 58%

P( X =x) =

=

X	P(X= x)
0	0.000000
1	0.000001
2	0.000011
3	0.000088
4	0.000514
5	0.002272
6	0.007842
7	0.021660
8	0.048605
9	0.089495
10	0.135948
11	0.170670
12	0.176765
13	0.150218
14	0.103722
15	0.057294
16	0.024725
17	0.008034
18	0.001849
19	0.000269
20	0.000019
Total	1

Probability that majority are sport utility. Majority will be more than 50%. Therefore 50% of 20 = 10

P( X > 10) = P(X= 11) + P(X = 12) .......P( X = 20)

P( X > 10) = 0.6936

The probability that a majority of them are sport utility vehicles.is 0.6936.