Question

State police believe that 40 % of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of the first

80 cars which pass the trap. Answer the following questions.

a) Using the 68-95-99.7 rule, draw and label the distribution of the proportion of these cars the police will observe speeding. Which graph shows the distribution of the proportion with the intervals for 68%, 95%, and 99.7%?

A.

0.20.40.6

A normal curve with horizontal axis from 0.2 to 0.6 in intervals of 0.02 is centered at 0.4. A dashed vertical line extends from 0.4 on the horizontal axis to the normal curve at its peak. The area below the curve is subdivided into three intervals by three pairs of solid vertical lines that extend from the horizontal axis to the normal curve and have horizontal coordinates as follows: 0.37 and 0.43; 0.35 and 0.46; 0.32 and 0.48. All values are approximate.

B.

0.20.40.6

A normal curve with horizontal axis from 0.2 to 0.6 in intervals of 0.02 is centered at 0.4. A dashed vertical line extends from 0.4 on the horizontal axis to the normal curve at its peak. The area below the curve is subdivided into three intervals by three pairs of solid vertical lines that extend from the horizontal axis to the normal curve and have horizontal coordinates as follows: 0.35 and 0.46; 0.29 and 0.51; 0.24 and 0.57. All values are approximate.

C.

0.40.60.8

A normal curve with horizontal axis from 0.4 to 0.8 in intervals of 0.02 is centered at 0.6. A dashed vertical line extends from 0.6 on the horizontal axis to the normal curve at its peak. The area below the curve is subdivided into three intervals by three pairs of solid vertical lines that extend from the horizontal axis to the normal curve and have horizontal coordinates as follows: 0.57 and 0.63; 0.55 and 0.66; 0.52 and 0.68. All values are approximate.

D.

0.40.60.8

b) Do you think the appropriate conditions necessary for your analysis are met? Are the conditions necessary to use a normal model met?

A.

Yes, all the conditions are met.

B.

No, the success/failure condition is not met.

C.

No, the 10% condition is not met.

D.

No comma the randomization and success divided by failure conditions are not met.No, the randomization and success/failure conditions are not met.

E.

No, the randomization and 10% conditions are not met.

F.

No, the 10% and success/failure conditions are not met.

G.

No comma the randomization condition is not met.No, the randomization condition is not met.

H.

No, none of the conditions are met.

Answer 1

Here we have

p = 0.4, n=80

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

(a)

Now,

Following is the graph:

b)

Since np(1-p) = 19.2 so  the 10% and success/failure conditions are met.

Sample is random sample.

Answer:

A. Yes, all the conditions are met.