Statistics and Probability Answers

A quality analyst wants to construct a sample mean chart for controlling a
packaging process. He knows from past experience that the process standard deviation
is two ounces. Each day last week, he randomly selected four packages and weighed
each. The data from that activity appear below.
Weight
Day Package 1 Package 2 Package 3 Package 4
Monday 23 22 23 24
Tuesday 23 21 19 21
Wednesday 20 19 20 21
Thursday 18 19 20 19
Friday 18 20 22 20
(a) Calculate all sample means and the mean of all sample means.
(b) Calculate upper and lower 2-sigma x-bar chart control limits that allow for
natural variations. [3 Marks]
(d) What is upper and lower control limit for the R-Chart?
(c) Based on the x-bar and R charts, is this process in control?

Among Ph.D. students

• 65% take the probability course.

• 25% take the data science course

• 206 take both probability and data science courses

If we select randomly a student,

1. What is the probability that she takes the data science course given that she takes the probability course? 2. What is the probability that she takes the probability course given that she takes the data science course? 3. What is the probability that she doesn't take the probability course given that she takes the data science course?

Suppose that a customer buys bread 1/2 of the time, buys butter 1/4 of the time, and both bread and butter 1/8 of the time.

1. What is the probability that he buys either bread or butter or both? 2. What is the probability that he buys neither bread nor butter?

4. An insurance company classifies the airplane it insures into class L (low risk)
and class H (high risk), and estimates the corresponding proportions of
the airplane as 70% and 30% respectively. The company has also found that 99%
of class L and 88% of class H airplane have no accident within a year. If an
airplane insured by the company has no accident within a year, what is the
probability that it belongs to
(a) class H?
(b) class L?

Of a company's employees, 30% are women and 6% are married women Suppose an employee is selected. at random. If the employee selected is a woman, what is the probability that she is married.?"

a. 0.2
b. 0.06
c. 0.3
d. 0.018

Assume that in a given region, 40% of young males are alcoholics. Find the probability that in a sample of 10 young males,
1. Only one young male is an alcoholic,
2. At most 2 are alcoholics.
3. More than 4 are alcoholics

A bag contains 4 red balls, 3 blue balls and 5 yellow balls If a ball is selected at random, find the probability that the ball will be blue or yellow.

a. 0.4167
b. 0.75
c. 0.3333
d. 0.6667

What is the probability that two female students will be selected at random, one after the other, to participate in a research project from a class of 7 male and 3 female students?

a. 0.0667
b. 0.3
c. 0.1
d. 0.2222

An experiment involves studying the composition of genders of a set of triplets What is the probability that there are 2 boys and a girl in the set?

a. 0.875
b. 0.125
c. 0.375
d. 0.625