Math Answers

Rick Douglas, the new manager of Food Barn, is

interested in the percentage of customers who are

totally satisfied with the store. The previous manager

had 86 percent of the customers totally satisfied, and

Rick claims the same is true today. Rick sampled 187

customers and found 157 were totally satisfied. At the

1 percent significance level, is there evidence that

Rick's claim is valid?

A multiple choice test consists of 8 questions with 

3 answers of each question. A student answers 

each question by rolling a dice and checking 

the first answer if he gets 1 or 2 then second answer 

3 or 4 and third if he gets 5 or 6.to get a distinction 

He/she must secure at least 75% correct answer. 

If there is no negative marking then 

Solve the probability that student secures distinction.

In a problem of testing of a simple hypothesis against a simple alternative, if the probability of type 1 error is known to be 0.06 then the power of test will be0.94. Is it true?

1. Find the fourier cosine Series for the function f(x)=x^2 for 0<x<π
2. Obtain a fourier expression for f(x)=x^2 for -π<x<π where f(x) is a even function

The average sale (no of burgers) of a fast food shop is 30 burgers/day. What is the

probability that exactly 50 burgers will be sold the next day? 

1. A Kelifa Business Centre plans to sell two models of an item at costs of $350 and $400. The $350 model yields a profit of $85 and the $400 model yields a profit of $90. The total demand per month for the two models will not exceed 150. Find the number of units of each model that should be stocked each month in order to maximize the profit. Assume the merchant can invest no more than $56,000 for inventory of these items.

A. Formulate Linear Programming problems (LPP)

B. Find the optimal solution by Graphic method

Suppose we roll two dice and let X be the maximum of the two numbers obtained and let Y be their minimum. Write down the distribution tables of X, Y and Z = (X, Y ).

A production facility contains two machines that are used to rework items that are initially defective. Let 𝑋 be the number of hours that the first machine is in use and let 𝑌 be the number of hours that the second machine is in use, on a randomly chosen day. Assume that 𝑋 and 𝑌 have a joint probability density function given by 𝑓(𝑥) = { 3 2 (𝑥 2 + 𝑦 2 ) 0 < 𝑥 < 1 𝑎𝑛𝑑 0 < 𝑦 < 1 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. a. What is the probability that both machines are in operation for less than half an hour?

The population of a certain state is known to grow at a rate proportional to the number of people presently living in the state. If after 10 years the population has trebled and if after 20 years the population is 150,000, find the number of people initially living in the state

There are four red, three green, and five blue discs. Find the probability that the two discs of same color are drawn out