A police department has deployed a fleet of 5 police officers to give speeding tickets during the last day of the current month. The police department wants to give a fixed fine for every speeding infraction. Each police officer has to measure the speed of 70 vehicles and the probability that a vehicle goes above the speed limit is 0.15.

Using the normal approximation and the continuity correction, determine the smallest fine, rounded to the nearest integer, that ensures the department will raise at least $7,000 with 95% certainty.

• $171
• $180
• $185
• $190
• $200

An insurer has classified a pool of policies into two classes: class A and class B. The probability of observing more than one claim during a single coverage period is zero for all policies and claim size is constant for all policies:

Using the normal approximation for aggregate losses, the insurer sets insurance rates at the lowest level that guarantees a profit 95% of the time.

Determine the rate for class B policyholders assuming that the expected profit % is the same for all policies.

• $12.16
• $12.77
• $13.31
• $26.09
• $30.65

A club serves dinner to members only. They are seated at 12-seat tables. The manager observes over a long period of time that 95 percent of the time there are between six and nine full tables of members, and the remainder of the time the numbers are equally likely to fall above or below this range. Assume that each member decides to come with a given probability [math]p[/math], and that the decisions are independent. What is [math]p[/math]?

• 0.04
• 0.055
• 0.063
• 0.07
• 0.075

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

A portfolio of annual policies are classified into two classes: class A and class B. You are given the following assumptions about the policies:

• Claim size is always 100 for class A policies and 200 for class B policies
• The probability of observing more than one claim per policy is zero for all policies in the portfolio
• The probability of observing a single claim in a year is 0.05 for class A policies and 0.03 for class B policies
• 25% of the policies in the portfolio belong to class A
• The expected loss for class A policies is 0.9 times the premium and the expected loss for class B policies is 0.8 times the premium.

Using the normal approximation, determine the smallest number of policies required in the portfolio that is divisible by 4 and large enough that the portfolio is profitable at least 95% of the time.

1. 1,020
2. 1,032
3. 1,672
4. 1,680
5. 1,688