# Statistical Process Control

Anonymous
timer Asked: Apr 3rd, 2017

Question description

• 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)

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