A hypothesis test was done on the mean cost of textbooks at UVA in a given semester. the null and alternative hypotheses were H₀: μ=$220 and H₁: μ < 220. A sample of 49 UVA students showed a mean of $212, and a P-value of 0.092 was calculated. The P-value is:

a) The probability of making the wrong decision

b) The probability that the true value is $212

C) The probability that if the true value is $220 we will have a sample mean of $212 or less

d) The probability that if the true value is $220 we will have a sample mean that is equal to $212

e) The probability that the true value is $220

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y , taking values in {0, 1, 2, 3} each (for a total of 16 possible points). Their joint probability mass function is given by fXY (x, y) = c · x+1 y+1 . Answer the following questions. (a) What is c? (b) What is the probability that X = Y ? (c) Derive the marginal probability mass functions for both X and Y . (d) What is the probability that X ≤ Y given that Y = 2? (e) What is the probability that X ≤ Y ?

A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.

Determine the probability that exactly 3 of these cards are Aces.

1. Answer:  %

Determine the probability that all five of these cards are Spades.

1. Answer:  %

Determine the probability that exactly 3 of these cards are face cards.

1. Answer:  %

Determine the probability of selecting exactly 2 Aces and exactly 2 Kings

1. Answer:  %

Determine the probability of selecting exactly 1 Jack.

1. Answer:  %

Q25.If the records show that, the probability of failing (with grade F) this course is p, what is the probability that at most 2 students out of 15 fail this course? {Hint: use binomial distribution}

Q26.If the records show that, the probability for a student to get a grade B this course is p, what is the probability that exactly 4 students out of 15 will have a grade B for the course? {Hint: use binomial distribution}

Q27.What is the probability of selecting a grade A student for the first time either in 2nd or 3rd selection?

DATA: A:11 B:2 C:1 D:0 F:1

It has been recently estimated that close to40% of Americans have brown eyes. A)Find the probability of having less than 6 brown eyed people in a group of12 Americans. B) Find the probability of having at least 11brown eyed people in a group of 19 Americans. C) Find the probability that in a group of 7 Americans, no one will have brown eyes. D) Find the probability that in a group of 15 Americans, no more than 3 will have brown eyes. E) In a group of 80 Americans, find the probability of having more than 30 brown eyed people.

Q1) Assume that the time takes you to prepare your morning coffee uniformly varies between 28 and 45 seconds. Calculate the following:)

Probability that your next cup of coffee will take more than 35 seconds  : ?

Probability of getting the same cup in less than 32 seconds  : ?

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Suppose the distribution is normally distributed with mean of 100 and a standard deviation of 15:

What is the probability that random variable has less than 115  : ?

What is the probability a random variable is greater than 131.5  : ?

What is the probability a random variable lies between 90 and 110  : ?

Q8. One store notes that the probability of some type of error in a telephone order is 0.2. A supervisor randomly selects telephone orders and carefully inspects each one.

1. (2pts) What is the probability that the third telephone order selected will be the first to contain an error?

2. (3pts) What is the probability that the supervisor will inspect between two and six (inclusive) telephone orders before finding an error?

3. (3pts) What is the probability that the inspector will examine at least seven orders before finding an error?

4. (4pts) Suppose the first four telephone orders contain no errors, what is the probability that the first error will be on the eighth order or later?

A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.

Determine the probability that exactly 3 of these cards are Aces. Answer: %

Determine the probability that all five of these cards are Spades. Answer: %

Determine the probability that exactly 3 of these cards are face cards. Answer: %

Determine the probability of selecting exactly 2 Aces and exactly 2 Kings Answer: %

Determine the probability of selecting exactly 1 Jack. Answer: %

A manufacturing operation utilizes three production lines to assemble electronic fuses. All lines produce fuses at the same rate and 20% of fuses are defective. Production lines recently suffered mechanical difficulty and probability of choosing a product from line 1 given defective is 40%, probability of choosing a product from line 2 given defective is 50%, and probability of choosing a product from line 3 given defective is 25%.

What is the probability that a customer buy a non-defective fuse produce by line 2?

What is the probability that a customer buy a fuse produce by line 3?