State police believe that 40 of the drivers traveling on a m

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.

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%.

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

1. yes all conditions are met

2. no the randomization and 10% conditions are met.

3. no the 10% condition is not met

4. no the randomization condition is not met

5. no the randomization and success/failure conditions are not met

6. no the success/failure condition is not met

7. no the 10% and success/failure conditions are not met

8. no none of the conditions are met

Solution

The 68%, 95%, and 99.7% rule is under the assumption of normal distribution.

a) Here n = 80 and p = 0.4. Hence, EX = 32, and Var(X) = 12.8, and sd(X) =3.578.

b) The option 4 is correct since the traffic cops are investigating the first 80 cars for overspeeding.