Mathematics, 01.07.2021 23:00 carlosiscr7

A venture capital company feels that the rate of return (X) on a proposed investment is approximately normally distributed with mean 30% and standard deviation 10%. (a) Find the probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
(c) What is the expected value of the return?
(d) Find the 75th percentile of returns.

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Answer from: ddaaaeeee3503

a) 0.0062 = 0.62% probability that the return will exceed 55%.

b) 0.3085 = 30.85% probability that the return will be less than 25%

c) 30%.

d) The 75th percentile of returns is 36.75%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 30% and standard deviation 10%.

This means that $\mu = 30, \sigma = 10$

(a) Find the probability that the return will exceed 55%.

This is 1 subtracted by the p-value of Z when X = 55. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55 - 30}{10}$

Z = 2.5

Z = 2.5 has a p-value of 0.9938

1 - 0.9938 = 0.0062

0.0062 = 0.62% probability that the return will exceed 55%.

(b) Find the probability that the return will be less than 25%

p-value of Z when X = 25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{25 - 30}{10}$

Z = -0.5

Z = -0.5 has a p-value of 0.3085

0.3085 = 30.85% probability that the return will be less than 25%.

The mean, that is, 30%.

(d) Find the 75th percentile of returns.

X when Z has a p-value of 0.75, so X when Z = 0.675.

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 30}{10}$

X - 30 = 0.675*10

X = 36.75

The 75th percentile of returns is 36.75%.

Answer from: Quest

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

(x^4) ^ ¼ = 81 ^ ¼

81 = 3^4 so (3 ^ 4) ^ ¼ = 3 ^ 1 = 3

by hand: (3 ^ 4) ^ ¼ = 3 ^ (4 x ¼) = 3 ^ 1 = 3 (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

How to find a number whose 4th power is 81 quickly?

Answer from: Quest

75%

step-by-step explanation:

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