The-probability-of-getting-a-letter-that-can-be-found-in-your-first-name-statistics-homework-help

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1.(15 points) Assume that the 26 letters of English language alphabet (A through Z) are the equally likely outcomes (simple events) of a statistical experiment, e.g., a wheel of fortune with 26 equal divisions (wedges of the same central angle size), each labeled a unique letter.The 26 different equally probable outcomes comprise the sample space S.

(a)Spell your complete name (first name and last name) in capital (upper case) letters:

I will spell out the name, but the letters are as follows: A, C, E, E, M, N, P R, S, S, T, U, Y

First Name:­ ……………

Last Name: …………….

(b)If we conduct the statistical experiment once (e.g., rotating the wheel introduced above), show your work to find

(b1) The probability of getting a letter that can be found in your first name

(b2) The probability of getting a letter that can be found in your last name

(b3) The probability of getting a letter that can be found in your first and last names

(b4) The probability of getting a letter that can be found neither in your first name nor in your last name

(b5) If we conduct the statistical experiment twice, what is the probability that we once get a letter that exists in your complete name?

2.9 points) A statistical experiment involves flipping a fair coin three times.

(a)Determine the sample space for the statistical experiment.The sample space is the set of all possible outcomes; for example, HTH is one possible outcome, where H stands for Heads and T stands for Tails.The format of your sample space (S) in set notation would look like

S = {HTH, …}

Hint: You may use a tree diagram to find all possible outcomes.

(b)Construct a two-column probability distribution table reflecting the values of random variable X, representing the number of possible heads (0, 1, 2, or 3), and their corresponding probabilities.

(c)Using your table, find the expected value of X, as E(X) = ∑(xi P(xi) = x1 P(x1) + x2 P(x2) + … + xn P(xn).

3.(10 points) A stamp collector has a set of four different stamps of different values and wants to take a picture of each possible subset of his collection (including the “empty set,” depicting just the picture frame!), i.e., pictures showing no stamps, one stamp, two stamps, three stamps, four stamps, or five stamps. In each picture showing two or more stamps, the stamps are in a row. Showing your work, determine the maximum number of different pictures possible, when the difference between two pictures would be either in the number of stamps or in the horizontal order of the stamps (order is important). For example, if the stamp collector had just two different stamps (say A and B) of different values, he would have five pictures showing: A, B, AB, BA, and the empty frame.

4.(13 points) Twenty-eight people have been invited to a party.Each invitee meets all other invitees, shaking hands.

(a)Determine the total number of the handshakes.

(b)If five invitees are from out of state and others are local, what is the probability of randomly selecting two invitees and those two are local.

5.(10 points)A telemarketing executive has determined, by surveying, that for a particular product, 22% of the people contacted will purchase the product. If 11 people are randomly contacted, what is the probability (to four decimal places) that at most 2 will buy the product? Show work/explanation.

Hint: The question is different from “what is the probability that 2 will buy the product”?

6.(13 points) The table below gives the distribution of blood types by sex in a group of 1,200 individuals.

Blood Type

Male

Female

Total

O

400

216

616

A

284

60

344

B

144

48

192

AB

36

12

48

Total

864

336

1200

(Answers for parts a through f can be stated as fractions, such as 35/46, or as decimals rounded to three decimal places)

A person is selected at random from the group.

Showing your work, what is the probability that the person:

(a) is female?

(b) has blood type A?

(c) is a female having blood type A?

(d) is a female or has blood type A?

(e) is female, given that the person’s blood type is A?

7.(30 points) Using graph(s), shading, and appropriate probability distribution table, and assuming that the heights of women are normally distributed, with a mean of 65.0 inches and a standard deviation of 2.5 inches, and assuming that men have heights that are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches,

(a)Calculate and write down your height in inches. Determine what percentage of people of your gender would be taller than you are. In case your height is “exactly” 65 inches, add 1 inch to it and work with 66 inches.

(b)If someone of your gender is randomly selected what is the probability that the selected person would be shorter than you are?

(c)What is the minimum height of a person of your gender to join the “Top 15% Tall Club”?

(d)If 144 people of your gender are randomly selected, determine the probability that their mean height would exceed your height.

(e)If 25 people of mixed gender, with a mean height of 67 inches and standard deviation of 2.60 inches are randomly selected from a normally distributed population, construct a 95% confidence interval for the mean of the population.

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