Math Answers

Perform the hypothesis of the following scenarios.

The graduate record exam is standardized test recquired to be admitted to many graduate schools in the United States. A high score in GRE makes admissions more likely. According th the educational testing service, the mean score for takers of GRE who do not have training courses is 555 with standard deviation of 139. Brain Philippine offers expensive GRE training courses, claiming their graduates score better than those who have not talen any training courses. To test the company's claim, a statisticiam randomly selected 30 graduates of BP and asked their GRE scores. They recorded a mean score of 560 in GRE. Is the company's claim true, using a 95% confidence level?

Find each of the following percentile points under the normal curve.

1. P99

2. P90

3. P68

4. P40

5. P32

Find each of the following percentile points under the normal curve. 1. P99 2. P90 3. P68 4. P40 5. P32

find the distance between the point (1, 2) and the line y= 4x+ 1

B. The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $1000 for the production setup. The variable cost is $30 per pair, and each pair sells for $40.

a. Let x indicate the number of pairs of shoes produced. Develop a mathematical mode

for the total cost of producing repairs of shoes.

b. Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes.

c. What is the breakeven point?

What is the value of this statement -B if B = F.

A. True

B. False

What is the value of this statement -(B VC) if B=F.C=T.

A. True

B. False

What is the value of this implication p→qif p = F and q = F.

A. True

B. False

Identify the graph of each of the following showing the centre, foci, length of the latus rectum, the eccentricity and asymptotes where applicable

I. 25x² + 4y² = 100

II. 25x² + 16y² = 400

A researcher wanted to estimate the difference between the percentages of users of two 

tooth pastes who will never switch to another tooth paste. In a sample of 500 users of 

Toothpaste A taken by this researcher, 100 said that they will never switch to another 

toothpaste. In a sample of 400 users of Toothpaste B taken by the same researcher 68 said 

that they will never switch to another toothpaste.

(i) Let p1 and p2 be the populations of all users of Toothpastes A and B, respectively who 

will never switch to toothpaste. What is the point of p1-p2? (4 marks)

(ii) Construct a 98% confidence interval for the difference between the proportions of all 

users of the two toothpastes who will never switch (6 marks)

Solve for the mean of the sampling distribution of the sample means