Math Answers

Potholes on a highway can be a serious problem, and are in constant need of repair.

With a particular type of terrain and make of concrete, past experience suggests that

there are, on the average, 2 potholes per mile after a certain amount of usage. It is

assumed that the Poisson process applies to the random variable “number of

potholes.”

a) What is the probability that no more than one pothole will appear in a section of

1 mile?

b) What is the probability that no more than 4 potholes will occur in a given section

of 5 miles?

The number of failures of a testing instrument from contamination particles on the

product is a Poisson random variable with a mean of 0.02 failure per hour.

a) What is the probability that the instrument does not fail in an 8-hour shift?

b) What is the probability of at least one failure in a 24-hour shift?

For a certain type of copper wire, it is known that, on the average, 1.5 flaws occur per

millimeter. Assuming that the number of flaws is a Poisson random variable, what is

the mean number of flaws in a portion of length 5 millimeters? What is the

probability, in 4 significant figures, that no flaws occur in a certain portion of wire of

length 5 millimeters?

The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean 𝜆 = 7. Compute the probability that more than 10 customers will arrive in a 2-hour period.

Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. Compute for the mean, variance, standard deviation. Construct a Probability histogram. *

9 points

find the centroid and boundaries y=x^2 and the line y=x

P(Z>-1.53)

Find the probability of getting a red ace when a card is drawn at random from an ordinary deck of cards.

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"

4.f (x) = "\\underset{x^-6}{=} -"____ x² + "\\sqrt[4]{x}"

Find each of the following percentiles points

under the normal curve.

1. P82

2. P34

3. P88

4. P42

5. P68