Math Answers

Suppose that Game store in Polokwane donated a lot of 8 computer sets that includes 3 which are malfunctioning or defective. If 4 of this computer sets are chosen at random for delivery to a school. i) What will be the probability mass function of a random variable � (3) ii) What will be the expected value of �

Prove that ((𝑝 → 𝑞) ⋀ ¬𝑞 ) → ¬𝑝 ) it’s tautology without using truth table?

Find the value of m for which the system of equations

x - 2y + z = 0,

-2x - y + 3z = 0

y + z = m 

has only trivial solution.

Find the class boundaries, midpoints, and size for each class.

(a)  32 – 38

(b)  86 – 104

(c)  895 – 905

(d)  12.3 – 13.5

(e)  3.18 – 4.96 

How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?

The heights of the population of boys are normally distributed with a mean of 66 inches and al standard deviation of 8.9 inches. If a random sample of 40 boys is drawn from this population, what is the probability that the mean of this sample is greater than 64.5 inches?

Express each of these statements using quantifiers: a) Every student in this class has taken exactly two mathematics classes at this school.

A sample size of 36 is to be selected from a population that has a mean of µ = 45 and standard deviation s of 10.

• Find the mean of the sampling distribution
• Find the standard error of the sampling distribution.
• What is the probability that this sample mean will be between 40 and 50?

The height of grade 1 pupils are approximately normally distributed with µ = 45 inches and s = 2.

• If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?
• A class of 30 of these pupils is used as a sample. What is the probability that the class mean is between 42 and 47?
• If a pupil is selected at random, what is the probability that is taller than 46 inches?
• A class of 30 of these pupils is used as sample. What is the probability that the class mean is greater than 46 inches?

Let A, B, and C be sets. Show that (A − B) − C =

(A − C) − (B − C).