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.You have 9 different pieces of Halloween candy in front of you. How many different ways could you order your arrangement of eating all the candy?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.A fair coin is tossed six consecutive times. What is the probability that the sequence will be heads, tails, heads, heads, tails, heads?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.Possible values of X àn = π =1 – π =The discrete probability distribution is:A fair coin is tossed six consecutive times. What is the probability that the sequence will have exactly 4 heads in it? A fair coin is tossed six consecutive times. What is the probability that the sequence will have at least 4 heads in it?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 Create a new variable called “Age Category” that splits the Age variable into the following four categories: Construct a cross tab for Age Category and Gender.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.)What is the average toothpaste use for males in the data?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. 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?If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine B?If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine C? USE THREE DECIMAL PLACES WHERE NEEDED X P(X) (Intentionally left blank to show work for problem #8e) Possible values of X àn = 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)