STAT quizzes 4-6

A fair die is rolled 100 times. We expect to see an odd number _____ times, give or take _____ or so.

(i) 50 (ii) 5

Suppose a number x is chosen from the numbers {-2, -1, 0, 1, 2} with equal probabilities. What will be the probability of x2 > 0?

0.8

Given an event E, if P(E happens) = 0.07, then P(E doesn't happen) =

0.93

The color distribution in a bag of Reese's Pieces was found to be 13 brown, 22 orange, and 15 yellow. If a piece is randomly drawn and replaced, what is the probability that it will take less than 8 draws to get an orange piece?

0.983

How many four-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 (Repetition of digits not allowed)?

6P4

How many ways can gold, silver, and bronze medals be awarded for a race run by 8 people?

8P3= 8!/ (8-3)!

We can apply central limit theorem for large number of draws from which of the following distributions?

All of the above

When n = 10000 and p = 0.001, the binomial probability distribution can be approximated by

Both A and B

You survey 500 people, asking if their eye color: brown, blue, green, or other. The random variable represents the eye color of each surveyed participant. The experiment is:

Not a binomial experiment. There are more than two outcomes.

If two events A and B are mutually exclusive, then

P (A or B) = P(A)+P(B)

Suppose 64% of the students in a school are boys. What is the chance that in a randomly selected sample of 400 students, the boy proportion is less than 60%? (Note: N(μ, σ) is a normal random variable with mean μ and SD σ).

P( N(0.64,0.024) < 0.6)

Suppose 60% of the American population is obese. What is the chance that in a randomly selected sample of 150 Americans, 67 are obese?

P(66.5≤N(90,6) ≤ 67.5)

A deck of cards is shuffled and the top two cards are placed face down on a table (this is equivalent to drawing without replacement). Are the following statements true or false? (i) P(first card is the ace of clubs) = 1/52 (ii) P(second card is the ace of diamonds) = 1/52 (iii) P(first card is the ace of clubs and the second card is the ace of diamond) = (1/52)*(1/52)

(i) and (ii) are true, (iii) is false

Past experience has shown the probability that a droid purchased from a super shop will not be faulty is 0.75 and that each droid purchased is an independent event. Luke needs to buy an unspecified number of droids. Find the probability that the first faulty droid will occur on the 4th droid purchased.

0.105

In a certain population, 40% of the adults experience hypertension at some point of their lives. Suppose 20 adults are randomly chosen from this population. What is the probability that at most 5 of them would have experienced hypertension?

0.1256

One graduate student is trying to stably transfect a cell line with a reporter construct. From previous experience with this system, we know that she has a 30% chance of success on each experiment (or trial). She will keep doing the experiments until one is successful. Assume each experiment is independent. What is the probability that she will conduct at least 3 experiments?

0.49

Two fair, six-sided dice are rolled. What is the probability that the sum of the numbers rolled is 3?

1/18

Nevada roulette wheel has 38 pockets: 0, 00, 1, 2, ..., 36. If you bet a dollar on a single number at Nevada roulette, and that number comes up, you get the $1 back together with winning of $35. If any other number comes up, you lose the dollar. Suppose you play roulette 100 times, betting a dollar on the number 17 each time. What is your expected value for the net gain?

100 * [1/38 * $35 + 37/38 * (-$1)]

Based on the table below, if one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker.

145/281

Panda express has a create-your-own combo dining option, where you can pick up 3 different entrées from 12 selections. In how many ways can you create your own combo menu?

220

Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E and F) = 0.3, then what will be the value of P(F | E)?

3/5

Alice flips a fair coin 10 times. Bob flips a fair coin 20 time independently. What is the probablity that the total number of heads Alice and Bob receive is 10?

30C10 * 0.5^10 * (1-0.5)^20

How many unique ways are there to arrange the letters in the word GLASS?

5C2*3P3

There are permutations of the 6 letters of the word "wordle". In how many of them is "r" the third letter?

5P5=5!

A die is rolled 100 times. What is the chance that the number of odd numbers will be in the range from 40 to 60? (Hint: use 68-95-99.7% rule.)

95%

You are drawing at random from a large box of red and blue marbles. Which of the following is FALSE?

As the number of draws goes up, the SE for the number of reds in the sample goes down.

Joanne who has not studied for the upcoming STAT 2332 quiz decides to 'wing it'. She does not know any answer and guesses on the 10 quiz questions. Every question has 4 choices: (A), (B), (C), (D). Let Y=the number of questions that she gets correct. Which distribution does the random variable, Y, follow?

Binomial distribution with n=10, p=1/4

According to government data, 20% of American children under the age of six live in households with income less than the official poverty level. A study of learning in early childhood chooses a sample of 300 children, they want to know the number of children in the sample who come from poverty-level households. Find the expected number of children in the sample who come from poverty-level households? And what is the corresponding SE?

EV = 60, SE = 6.93

We draw three tickets at random without replacement from the box. 1 2 3 4 5 Let X be the number of ticket "5" among the selected three tickets. What is the distribution of X?

None of the above

Based on the table below, if one of the 1124 people is randomly selected. Let event A= the person is a man and event B= the person is a heavy smoker. What can we say about the two events?

They are dependent because P(B|A)≠P(B).

Suppose we draw n times with replacement from the following box. 0 0 0 1 1 Let X be the number of times that 1 is drawn. The Law of Averages says that, as n increases,

X / n gets close to a constant

One hundred random draws are made with replacement from the box: -1 -1 -1 1 2 John claims that the expected value for the average of the draws is 0. Is his claim correct?

Yes, because the average number of the box is (-1-1-1+1+2)/5.

Which of the tables below represents a probability distribution for a discrete random variable? X P(X) -1 0.1 0 0.2 1 0.3 2 0.4 Y P(Y) 1 0.2 2 0.1 3 0.35 4 0.45

only X

If two events A and B are mutually exclusive, then

they are not independent