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2023-03-26A 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?

0.168

0.001

0.231

0.667

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

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%

34.19%

10.95%

9.64%

14.36%

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

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?

.380

.562

.401

.541

Binomial distribution:

n = 25, r = 10, p = 0.4, q = 0.6

Summing up: 0.3799

2023-03-23

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?

8 years

10 years

11 years

9 years

If it takes n years for the growth, then:

1,000 = 710(1 + 3.5%)

Solving for n gives 9.96 years.

2023-03-22

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?

0.410

0.250

0.500

0.026

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: