Question

In: Statistics and Probability

The quarterly returns for a group of 59 mutual funds with a mean of 3.8​% and...

The quarterly returns for a group of 59 mutual funds with a mean of 3.8​% and a standard deviation of 6.9​%

can be modeled by a Normal model. Based on the model

​N(0.038,0.069​), what are the cutoff values for the

a) highest 10​% of these​ funds?

​b) lowest 30​%?

​c) middle 20​%?

​d) highest 70​%?

Solutions

Expert Solution

a) P(X > x) = 0.1

or, P((X - )/ > (x - )/) = 0.1

or, P(Z > (x - 0.038)/0.069) = 0.1

or, P(Z < (x - 0.038)/0.069) = 0.9

or, (x - 0.038)/0.069 = -1.28

or, x = -1.28 * 0.069 + 0.038

or, x = -0.05032

b) P(X < x) = 0.3

or, P((X - )/ < (x - )/) = 0.3

or, P(Z < (x - 0.038)/0.069) = 0.3

or, (x - 0.038)/0.069 = -0.52

or, x = -0.52 * 0.069 + 0.038

or, x = 0.00212

c) P(X < x) = 0.4

or, P((X - )/ < (x - )/) = 0.4

or, P(Z < (x - 0.038)/0.069) = 0.4

or, (x - 0.038)/0.069 = -0.25

or, x = -0.25 * 0.069 + 0.038

or, x = 0.02075

P(X > x) = 0.4

or, P((X - )/ > (x - )/) = 0.4

or, P(Z > (x - 0.038)/0.069) = 0.4

or, P(Z < (x - 0.038)/0.069) = 0.6

or, (x - 0.038)/0.069 = 0.25

or, x = 0.25 * 0.069 + 0.038

or, x = 0.05525

d) P(X > x) = 0.7

or, P((X - )/ > (x - )/) = 0.7

or, P(Z > (x - 0.038)/0.069) = 0.7

or, P(Z < (x - 0.038)/0.069) = 0.3

or, (x - 0.038)/0.069 = -0.52

or, x = -0.52 * 0.069 + 0.038

or, x = 0.00212


Related Solutions

The quarterly returns for a group of 74 mutual funds with a mean of 1.1​% and...
The quarterly returns for a group of 74 mutual funds with a mean of 1.1​% and a standard deviation of 4.9​% can be modeled by a Normal model. Based on the model ​N(0.011​,0.049​), what are the cutoff values for the ​a) highest 20% of these​ funds? ​b) lowest 40%? ​c) middle 80​%? ​d) highest 60%?
The quarterly returns for a group of 58 mutual funds with a mean of 3.4​% and...
The quarterly returns for a group of 58 mutual funds with a mean of 3.4​% and a standard deviation of 4.3​% can be modeled by a Normal model. From these​ funds, find the cutoff return​ value(s) that would separate the ​ a) highest 30​%. ​b) lowest 40​%. ​c) middle 60​%. ​d) highest 60​%. ​a) Select the correct choice and fill in any answer boxes in your choice below. ​(Round to two decimal places as​ needed.) A. nothing​%less thanxless than nothing​%...
The quarterly returns for a group of 53 mutual funds with a mean of 2.1​% and...
The quarterly returns for a group of 53 mutual funds with a mean of 2.1​% and a standard deviation of 5.1​% can be modeled by a Normal model. Based on the model ​N(0.021​,0.051​), what are the cutoff values for the ​ a) highest 10​% of these​ funds? ​ b) lowest 20​%? ​c) middle 40​%? ​d) highest 80​%?
1. Suppose the returns of a particular group of mutual funds are normally distributed with a...
1. Suppose the returns of a particular group of mutual funds are normally distributed with a mean of 9.7% and a standard deviation of 3.8%. If the manager of a particular fund wants to be sure that his fund is NOT in the bottom 25% of funds with the lowest return, what return must his fund have? (please round your answer to 2 decimal places). 2. Suppose the following data show the prices of 4 cars with similar characteristics that...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 0.8​% with a standard deviation of 4.9​%. Consider the Normal model ​N(0.008​,0.049​) for the returns of these mutual funds. ​a) What value represents the 40th percentile of these​ returns? ​b) What value represents the 99th​ percentile? ​c) What's the​ IQR, or interquartile​ range, of the quarterly returns for this group of​ funds?
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 2.1​% with a standard deviation of 6.5​%. If a normal model can be used to model​ them, what percent of the funds would you expect to be in each​ region? Use the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely. Be sure to draw a picture first. ​a) Returns of negative 4.4​% or less ​b)...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 5.9% with a standard deviation of 7.1​%. If a normal model can be used to model​ them, what percent of the funds would you expect to be in each​ region? Use the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely. Be sure to draw a picture first. ​a) Returns of negative −1.2​% or less ​b)...
For the third quarter (Q3) of 2014, a group of 163 mutual funds had a mean...
For the third quarter (Q3) of 2014, a group of 163 mutual funds had a mean return of 4.6% with a standard deviation of 5.1%. A histogram of fund returns shows a unimodal, symmetric shape. (Enter your answer to two decimal places.) (a) What return is necessary for a fund to be classified among the top 25%? % (b) What return is necessary for a fund to be classified among the bottom 10%? % (c) What return is necessary for...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return...
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 1.9​% with a standard deviation of 6.3​%. Consider the Normal model ​N(0.019​,0.063​) for the returns of these mutual funds. ​ a) What value represents the 40th percentile of these​ returns? ​ b) What value represents the 99th​ percentile? ​c) What's the​ IQR, or interquartile​ range, of the quarterly returns for this group of​ funds?
You are considering two mutual funds as an investment. The possible returns for the funds are...
You are considering two mutual funds as an investment. The possible returns for the funds are dependent on the state of the economy and are given in the accompanying table. State of the Economy Fund 1 Fund 2 Good 42 % 46 % Fair 18 % 25 % Poor −4 % −17 % You believe that the likelihood is 10% that the economy will be good, 40% that it will be fair, and 50% that it will be poor. a....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT