What is another way to write<br> (5-x)

A venture capital company feels that the rate of return (X) on a proposed investment is approximately normally distributed with

serious [3.7K]

Answer:

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%.

(c) What is the expected value of the return?

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%.

7 0

3 years ago

Sandra is a cake designer

artcher [175]

36.5
Hope this gets you where you want

7 0

4 years ago

Can someone please help! I don’t understand this

Phoenix [80]

Volume=530.14 , rounded to the nearest whole number would just be 530 ft.

3 0

3 years ago

State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else chan

Hatshy [7]

Answer:

Step-by-step explanation:

The formula for determining confidence interval is expressed as

Confidence interval

= mean ± z × s/ √n

Where

z is the value of the z score

s = standard deviation

n = sample size

a) The 95% confidence level has a z value of 1.96

The 99% confidence level has a z value of 2.58

Since 99% confidence level z value is greater than 95% confidence level z value, if we input it into the formula, it will result to a higher confidence interval. So changing from a 95% confidence level to a 99% confidence level would make a confidence interval wider.

b) The √15 is smaller than the √350. This means that if we make use of the formula, √350 will give a lower confidence interval than that of √15. Therefore, the confidence interval would be narrower changing from a sample size of 15 to a sample size of 350.

c) Applying the formula, a standard deviation of 15 pounds would result to a lower confidence interval than a standard deviation of 20 pounds. Therefore, the confidence interval would be wider changing from a standard deviation of 15 pounds to a standard deviation of 20 pounds.

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3 years ago

How do you solve this equation: 2n=4x+2y;y?

Natali5045456 [20]

How do you solve this equation:2n=4x+2y;y? Add answer+5 pts

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3 years ago

What is another way to write (5-x)