Math Answers

Solve the following problems by using Binomial formula:

i. If n = 4 and p = 0.10, P(X = 3) = ?

ii. If n = 7 and p = 0.10, P(X = 4) = ?

iii. If n = 10 and p = 0.10, P(X  7) = ?

iv. If n = 12 and p = 0.10, P(5  X  7) = ?

A discrete random variable X is believe to follow a binomial distribution b(x; 5, p). If P(X = 0) = 243/1024, then find P(X = 3).

Is it possible to have a Binomial Distribution in the following cases:

i. Mean = 5 and Variance = 2.5

ii. P(X = – 2) = 0.1467

iii. P(X less than or not equal to 1) = 0.18

iv. Three parameters i.e. n, p and q

v. P(X = 1) = 0.35

vi. P(X Greater than or equal to 1) = 1.27

vii. .P(X = 3.5) = 0.19

viii. P(1   less than or not equal to   X     less than or not equal to    4) = 0.79.

The lifetimes of a certain type of electrical components are distributed with a mean of 800 hours and standard deviation of 160 hours.If the manufacturer wishes to replace only 1 percent of the component that have the shortest life .what value should be used as the guaranteed lifetime

Use the Laplace transform to solve the given initial-value problem.

y′ + 2y = sin 4t, y(0) = 1

A. Find the finite population correction factor given the following:

(Show your solutions)

1.   N=400,n=40

Which of the following is part of the set of all possible rational zeros of

f(x)=2x4−x3+6x2−5x−8?

i.

±1; ±2; ±12; ±14

ii.

±1; ±2; ±4

iii.

±1; ±2; ±4; ±12; ±14

iv.

None of the given options.

v.

±2; ±8; ±14

According to the May 16,2017 report by Pew Research, 68% of US adults say solar energy is very effective in minimizing air pollution. A sample of 240 U.S adults are surveyed. Let p

ˆ

p^ be the sample proportion of Americans who believe solar energy is very effective in minimizing air pollution. 

1. What is the population proportion? Answer (decimal form)
2. What is the sample size? Answer
3. What is the mean of the sampling proportion? Answer
4. What is the standard deviation of the sampling proportion? Answer

(Round to 4th decimal place)

1- Find the domain of function f(X)=ln (-2/X2-x-6) +√x2 -1

2- Find the inverse function of the function f(X)=X2 -4x +5; X €(3,4)

3- construct the tangent line to the graph of the function f(X)= 4x.√x-2 .√x which is parallel to the line y=x.

Representation of intergers

Change the following number systems to base-10 numbers.

• 1101101001₂
• 5522₈
• 12CF₁₆