Statistical Process Control
- Standardize the subset of data below. The mean of the entire data set is 8 and the sample standard deviation is 2.
- Using the data from the Excel file on Canvas titled “HW 4” (worksheet titled “Problem 1”), answer the questions below. I would suggest using Excel to help with the solutions. Create a new variable called “Age Category” that splits the Age variable into the following four categories:
- A fair coin is tossed six consecutive times. Complete the components below to determine the discrete probability distribution below if we define X = # heads. Obviously this is a Bernoulli process. SHOW YOUR WORK TO RECEIVE MOST OF THE CREDIT FOR THIS PROBLEM. YOU HAVE AMPLE SPACE ON THE NEXT PAGE.
- n =
- π =
- 1 – π =
- The discrete probability distribution is:
- Now you flip an UNFAIR coin six consecutive times. This coin lands heads 85% of the time and tails 15% of the time. Complete the components below to determine the discrete probability distribution below if we define X = # heads. Despite the unfairness of the coin results, this is obviously still a Bernoulli process. SHOW YOUR WORK TO RECEIVE MOST OF THE CREDIT FOR THIS PROBLEM. YOU HAVE AMPLE SPACE ON THE NEXT PAGE.
x | z |
8 | |
13 | |
12 | |
6 | |
4 | |
4 | |
10 | |
2 | |
8 | |
14 | |
7 | |
3 | |
12 |
- Construct a cross tab for Age Category and Gender.
- What is the average toothpaste use for males between 20 and 39 in the data?
- What is the average toothpaste use for females in the data?
- What is the average toothpaste use for females between 40 and 59 in the data?
- Make a pivot table using Age Category and Gender to split the data. Report the maximum Toothpaste Use inside the table.
Make a pivot table using Age Category and Gender to split the data. Report the average Toothpaste Use inside the table. (One decimal place for your answer will suffice.)
C What is the average toothpaste use for males in the data?
How many different ways can the first 9 cards of a shuffled deck be ordered?
How many different combinations are there for the first 9 cards of a shuffled deck (note that order does not matter here)?
There are three machines that produce pencils in my factory. Machine A produces defective pencils 1% of the time, machine B produces defective pencils 5% of the time, and machine C produces defective pencils 12% of the time. Of the total output from these machines, 70% of the produced pencils are from machine A, 20% are from machine B, and the remaining 10% are from machine C. One pencil is chosen at random from the daily production.
- What is the prior probability that the pencil came from machine A?
- What is the prior probability that the pencil came from machine B?
- What is the prior probability that the pencil came from machine C?
- What is the conditional probability that the pencil is defective, given that it came from machine A?
- What is the conditional probability that the pencil is defective, given that it came from machine B?
- What is the conditional probability that the pencil is defective, given that it came from machine C?
- If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine A?
H If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine B?
I If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine C?
A fair coin is tossed six consecutive times. What is the probability that the sequence will be heads, tails, heads, heads, tails, heads?
Possible values of X à
USE THREE DECIMAL PLACES WHERE NEEDED
X | P(X) |
(Intentionally left blank to show work for problem #8e)
A fair coin is tossed six consecutive times. What is the probability that the sequence will have exactly 4 heads in it?
E A fair coin is tossed six consecutive times. What is the probability that the sequence will have at least 4 heads in it?
- Possible values of X à
- n =
- π =
- 1 – π =
- The discrete probability distribution is:
USE THREE DECIMAL PLACES WHERE NEEDED
X | P(X) |
(Intentionally left blank to show work for problem #9e)