A quantitative data set of size 80 has mean 30 and standard deviation 5. At least how many observations lie between 15 and 45?

At least 71 observations must lie inside the interval (15, 45).

Step-by-step explanation:

According with the Chebyshev’s Theorem, for any data set, the proportion (or percentage) of values that fall within k standard deviations from mean (that is, in the interval ) is at least , where k > 1.

Given:

The interval (15, 45) is the one that is formed by adding and subtracting three standard deviations from the mean.

By Chebyshev’s Theorem, at least of the data are within this interval. Since of 80 is 71.11, this means that at least 71.11 observations are in the interval. But one cannot take a fractional observation, so we conclude that at least 71 observations must lie inside the interval (15, 45).

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.

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%