You would like to make a nutritious meal of eggs, edamame and elbow macaroni. The meal should provide at least 30g of carbohydrates, at least 20g of protein, and no more than 60g of fat. An egg contains 2g of carbohydrates, 17g of protein, and 14g of fat. A serving of edamame contains 12g of carbohydrates, 12g of protein and 6 g of fat. A serving of elbow macaroni contains 43g of carbohydrates, 8g of protein, and 1g of fat. An egg costs $2, a serving of edamame costs $5, and a serving of elbow macaroni costs $3. Formulate a linear optimization model that could be used to determine the number of servings of egg, edamame, and elbow macaroni that should be in the meal in order to meet the nutrition requirements at minimal cost.

Question 10:

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 494 and a standard deviation of 39.

According to the standard deviation rule, approximately 68% of the students spent between $_____ and $ ______ on textbooks in a semester.

Question 11:

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 16.

According to the standard deviation rule, _____ % of people have an IQ between 52 and 148. Do not round.

Question 12:

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 19.

According to the standard deviation rule, only ______ % of people have an IQ over 157.

Question 13:

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 429 and a standard deviation of: σ= 23.

According to the standard deviation rule, almost 16% of the students spent more than what amount of money on textbooks in a semester?

Running times (Y) and maximal aerobic capacity (X) for 14 female
Runners. Data collected for running times and maximal aerobic capacity are listed
below
X: 61.32 55.29 52.83 57.94 53.31 51.32 52.18 52.37 57.91 53.93 47.88 47.41
47.17 51.05
Y: 39.37 39.80 40.03 41.32 42.03 42.37 43.93 44.90 44.90 45.12 45.60 46.03
47.83 48.55
(a) Calculate the mean, median, MAD, MSD, and standard deviation for each
variable. ? [Include all your steps and explain all the steps involved in details]
(b) Which of these statistics give a measure of the center of data and which give a
measure of the spread of data? [Explain in your own words]
(c) Calculate the correlation of the two variables and pro-duce a scatterplot of Y
against X. [Use excel for scatterplot, show all your computations concerning
the correlation and explain all your steps]
(d) Why is it inappropriate to calculate the autocorrelation of these data? [Explain in
your own words]

PLEASE SHOW ANSWER WORKED CALCULATIONS ON EXCEL AS PER QUESTION REQUIREMENTS.

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

5.54 A survey by Frank N.Magid Associates revealed that 3% of Americans are not connected to the Internet at home. Another researcher randomly selects 70 Americans. a. What is the expected number of these who would not be connected to the Internet at home?
b. What is the probability that eight or more are not connected to the Internet at home? c. What is the probability that between three and six (inclusive) are not connected to the Internet at home?

5.51 An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande River.Suppose six of the office workers are randomly selected. a. What is the probability that all six workers commute from the west side of the Rio Grande?

b. What is the probability that none of the workers commute from the west side of the Rio Grande?

c. Which probability from parts (a) and (b) was greatest? Why do you think this is?

d. What is the probability that half of the workers do not commute from the west side of the Rio Grande?

Alice and Bob are supposed to meet in the cafeteria. Alice arrives at a random time between
noon and 1pm, and wait for 15 minutes upon her arrival and then leaves. Bob also also arrives
at a random time between noon and 1 pm, but waits up to 20 minutes and then leaves.
(a) What is the probability that Bob arrives before 12:20?
(b) What is the probability that Alice and Bob meet?
(c) If Bob arrives later than Alice, what is the probability that they meet?
(d) Suppose that Alice and Bob have managed to meet. What is the probability that Bob
has arrived before 12:20?

Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6,P(B) = 0.4,and P(A ∩ B) = 0.3,suppose that P(C) = 0.2,P(A ∩ C) = 0.12,P(B ∩ C) = 0.1, and P(A ∩ B ∩ C) = 0.08.

a)What is the probability that the selected student has at least one of the three types of cards?

b)What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card?

c)Calculate P(B | A)and P(A | B).

P(B | A)=

P(A | B)=

d)If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard?

e)Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?

A bias coin has the probability 2/3 of turning up heads. The coin is thrown 4 times.
(a) What is the probability that the total number of heads shown is 3?
(b) Suppose that we know that outcome of the first throw is a head. Find the probability
that the total number of heads shown is 3.
(c) If we know that the total number of heads shown is 3, find the probability that the outcome
of the first throw was heads.

At a Midwestern business school, historical data indicates that 70% of admitted MBA students ultimately join the business school’s MBA program. In a certain year, the MBA program at the University admitted 200 students.

a. Find the probability that at least 150 students ultimately join the MBA program.

b. Find the probability that no less than 135 and no more than 160 students finally join the MBA program.

c. How many students should the MBA program expect to join the program?

d. What is the standard deviation of the number of students who will join the MBA program? e. Let X be the number of students out of 200 who will join the program. Would the empirical rule apply to the probability distribution of X in this case?

A population of young people was studied where the variable weight has an average of 60 kilograms. The standard deviation is 5 kilograms, and the serura variable presented an average cone of 1.70 meters and its standard deviation 10 centimeters. Calculate the probability of finding young people weighing over 58 kilograms and measuring less than 1.80 meters.

Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 85 and a standard deviation of 20. Use the​ 68-95-99.7 rule to find the following quantities.

a. The relative frequency of rates less than 125 using the​ 68-95-99.7 rule is ____________.

b. The relative frequency of rates greater than 105 using the​ 68-95-99.7 rule is ___________.

c. The relative frequency of rates between 45 and 85 using the​ 68-95-99.7 rule is _____________.

Consider a population of 10241024 mutual funds that primarily invest in large companies. You have determined that muμ​, the mean​ one-year total percentage return achieved by all the​ funds, is 8.408.40 and that sigmaσ​,the standard​ deviation, is 3.503.50. Complete​ (a) through​ (c). a. According to the empirical​ rule, what percentage of these funds is expected to be within ​±33 standard deviations ,deviations of the​ mean? 99.799.7​% b. According to the Chebyshev​ rule, what percentage of these funds are expected to be within

​±22 standard deviations of the​ mean? -75.075.0​% ​(Round to two decimal places as​ needed.)

***** c. According to the Chebyshev​ rule, at least

88.8988.89​%

of these funds are expected to have​ one-year total returns between what two​ amounts?

Between_ and _.

RegionExpected
Actual
Southeast

Defined

10098

Open

100104Northeast

Defined

150188

Open

150214Midwest

Defined

125120

Open

125108Pacific

Defined

200205

Open

200278

Report your findings from each Chi-square test that you conducted.

Based solely on the Chi-square test, discuss whether the company should accept the null hypothesis in each region or reject it in favor of the alternate hypothesis.

Discuss any other statistical analyses you would want the company to contemplate before deciding if it will go with a defined or open sales strategy.

Describe and discuss at least 1 other business scenario in which you believe Chi-square testing would be h