Astatistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.049.0 and 59.059.0 minutes. find the probability that a given class period runs between 50.2550.25 and 51.051.0 minutes.

0.075

Step-by-step explanation:

Let X be the length of a class of the statistics professor. Then, the probability density  function of X is given by

for x in the interval [49, 59]

because the lengths of her classes are uniformly distributed between 49 and 59 minutes.

We find the probability that a given class period runs between 50.25 and 51.0 minutes,

in the following way

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

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%