The amount of time it takes Annie to make dinner is continuous and uniformly distributed between 19 minutes and 49 minutes. What is the probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner

The probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner is 0.04.

Step-by-step explanation:

Let X = amount of times (in minutes) it takes Annie to make dinner.

The random variable X follows a continuous Uniform distribution with parameters a = 19 minutes and b = 49 minutes.

The probability density function of continuous Uniform distribution is:

Compute the value P (39 < X < 40 | X < 44) as follows:

Thus, the probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner is 0.04.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%