Statistics and Probability Answers

What is the probability that two female students will be selected at random to
participate in a certain research project, from a class of seven males and three
female students?

A class consists of 100 students, 60 students like music, 70 students like football,
and 30 students like football and music. A student is chosen randomly, what is
the probability that:
a. He likes music only.
b. He doesn't like music or football.
c. He doesn't like music and football.

A deck of playing cards, what is the probability of drawing either a black card or a
6 in a single draw?

Suppose the mean amount of cholesterol in eggs labeled “large” is 186 milligrams, with standard deviation 7 milligrams. Find the probability that the mean amount of cholesterol in a sample of 144 eggs will be within 2 milligrams of the population mean.

Given the probability distribution of infinite population below
X = x 1 2 3 4 5 Total
P(X = x) 1/5 1/5 1/5 1/5 1/5 1
a. Assuming that you sample without replacement, select all possible samples of
size 2 and set up the sampling distribution of the mean. Compute the mean of all
the sample means and also compute the population mean. Are they equal? What
is this property called?
b. Do (a) for a possible sample of size 3.
c. Compare the shape of the sampling distribution of the mean obtained in (a) and
(b). Which sampling distribution seems to have less variability, those in (a) or
(b)? Why?

2. Patients arrive at a hospital accident and emergency department at random follow a Poisson distribution at a rate of 6 per hour.
(a) Find the probability that, during any 90-minute period, the number of patients arriving at the hospital accident and emergency department is
(i) exactly 7 (2 marks) (ii) at least 3 (2 marks)
(b) What is the mean and standard deviation of the number of patients arriving at the hospital accident and emergency department in an hour? (2 marks)

1. The probability of telesales representative making a sale on a customer call is 0.15. Find the probability that
(a) no sales are made in 10 calls, (2 marks) (b) more than 1 sales are made in 20 calls. (3 marks)
Representatives are required to achieve a mean of at least 5 sales each day.
(c) Find the least number of calls each day a representative should make to achieve this requirement. (1 mark) (d) Calculate the least number of calls that need to be made by a representative for the probability of at least 1 sale to exceed 0.95.

A coin is flipped until 3 heads in succession occur.
List only those elements of the sample space that
require 6 or less tosses. Is this a discrete sample space?
Explain.