Question: A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine.
If the claim is true, what is the probability that 8 patients have relief within a few minutes?
Select an Answer: 0.168 0.001 0.231 0.667
Rationale:
This is a binomial probability. The probability of getting r successes out of n trials where the probability for success of each trial is p and the probability for failure of each trial is q (where q = 1 − p) is given by:
Here, n = 12, r = 8, p = 0.7 and q = 0.3. Therefore, we have:
2023-03-25
Question: An intern with Churn Brothers Brokerage has been instructed to calculate the coupon rate on an inverse floater. Assume the following information:
Reference rate = LIBOR = 6.75% per year
K = 12% per year
L = 35%
Using this information, what is the current annual coupon rate on this inverse floater?
Select an Answer: 34.19% 10.95% 9.64% 14.36%
Rationale:
The equation used to determine the coupon rate on an inverse floater is as follows:
Coupon rate = K − L × Reference rate
In this example, all the necessary information has been provided, and the calculation of the coupon rate is as follows:
Coupon rate = 12% − 0.35(6.75%) = 9.638%
Inverse floaters are debt instruments which have a coupon rate that moves inversely with a quoted reference rate, i.e., as the reference rate X increases, the coupon rate on an inverse floater tied to X would decrease.
2023-03-24
Question: David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one hour period twenty-five customers buy gasoline at this station.
What is the probability that more than ten and less than fifteen customers pay in cash?
Select an Answer: .380 .562 .401 .541
Rationale:
Binomial distribution:
n = 25, r = 10, p = 0.4, q = 0.6
Summing up: 0.3799
2023-03-23
Question: A bank savings account offers a savings rate of 3.5% per year, compounded annually.
How long would it take for an investment of $710 to grow to $1,000?
Select an Answer: 8 years 10 years 11 years 9 years
Rationale:
If it takes n years for the growth, then:
1,000 = 710(1 + 3.5%)n
Solving for n gives 9.96 years.
2023-03-22
Question: An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5.
Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?
Select an Answer: 0.410 0.250 0.500 0.026
Rationale:
This is a binomial probability. The probability of getting r successes out of n trials where the probability of success for each trial is p and the probability of failure for each trial is q (where q = 1 − p) is given by:
Here n = 4, r = 3, p = 0.20, and q = 0.80. Therefore, we have:
