Using Inequality Notation
Binomial Distribution
Geometric Distribution
Normal Approximation
Discrete Random Variables
100

In a distribution with X values ranging from 0 to 20, what values of the discrete variable X would be included in x< 4?

0, 1, 2, 3

100
The probability that a 3 year old battery works is .7 and a graphing calculator requires 4 batteries to work. Mrs. Owens finds 4 batteries that are 3 years old in the back of her closet. What is the probability that she puts them in a calculator and it works?
.2401
100

Jeremy takes a guesses on a multiple choice test in Chinese. Each question has options a, b, c, d, e, and f. What is the average number of questions he has to answer before he gets one correct?

Hint: This uses the formula for geometric mean!

6

100
Suppose X has a binomial distribution with n = 500 and p = .3. Find the mean and standard deviation of the distribution.
Mean =150 Standard Deviation = 10.25
100

Flip a coin four times. If Z = the number of tails in four flips, then the probability distribution of Z is

Z          0         1        2        3        4
P(Z)  .0625    .25     .375    .25   .0625

This expression represents the probability of at least one tail.

P (Z > 1)

200

P(x > 3) is equivalent to 1 - P(x < 3) when x represents a discrete variable. What is P(x > 7) equivalent to when x represents a discrete variable?

1 - P(x < 6)

200
The probability that a telemarketing employee reaches a live person is .11. Suppose they call 20 people in a night. What is the probability that they reach at least 5 people?
.061
200
On Jeremy's multiple choice test, what is the probability that the first time he gets one right is on the 4th question?
.096
200

Suppose the height Y of a crop of wheat has a Normal Distribution with the average height being 30 inches and standard deviation being 2.5 inches.
Compute P (32 < Y < 35).

Hint: You will need to find z-scores and use Table A!

.1891

200

Flip a coin four times. If Z = the number of tails in four flips, then the probability distribution of Z is

Z          0         1        2        3        4
P(Z)  .0625    .25     .375    .25   .0625

The probability of at least one tail is

0.9375

300
Suppose the probability of failing a lie detector test is 30%. In a 12-man jury, what is the probability that more than 3 people will fail the lie detector test?
.507
300

(n choose 5) p^5 (.71)^8 What is n? What is P? What is mean of the distribution?

n = 13 p = .29 Mean = 3.77

300

A basketball player has a history of making his free throws 45% of the time. What is the probability that he will make his first free throw on his 6th try in a game?

.022

300

In the 1997 Center for Disease Control, 20% of teenagers carry a weapon of some sort. Suppose that 300 teenagers walked into the drivers license facility on a given day. What is the probability that more than 50 of them carried some sort of weapon?

Hint: Find mean and SD, then z-score and use Table A!

.9265

300

Flip a coin four times. If Z = the number of heads in four flips, then the probability distribution of Z is

Z          0         1        2        3        4
P(Z)  .0625    .25     .375    .25   .0625

The mean of this distribution is

2

400
According to government data, 20% of employed women have never been married. 25 employed women are selected at random. Find the probability that the number of employed women who have never been married is greater than 3.
.766
400
It is estimated that 10% of drivers turn on their blinker before changing lanes. In a random sample of 4 drivers, what is the probability that at least one person uses his or her blinker when changing lanes?
.3439
400

A quarterback completes 47% of his passes. Construct a probability distribution table (out of n = 5) for the number of passes attempted before the quarterback has a completion

n        1         2        3        4       5 

P(n)  .47    .2491  .1320   .07   .037

400

What is the 10% condition?

n < 1/10N

(Sample size must be no larger than 10% of the population)

400

Flip a coin four times. If Z = the number of heads in four flips, then the probability distribution of Z is

Z          0         1        2        3        4
P(Z)  .0625    .25     .375    .25   .0625

This standard deviation of this distribution is

1

500
According to government data, 20% of employed women have never been married. 25 employed women are selected at random. Find the probability that the number of employed women who have never been married is within 1 standard deviation of its mean.
.793
500

A college basketball player makes 80% of her free throws. Her team is losing by two, and she is fouled shooting a 3-pointer. Assuming free throw attempts are independent, what is the probability that she makes at least two of the three free throws?

0.896

500

A poll shows that 60% of the adults in a town are Democrats. A newspaper reporter wants to interview a local democrat regarding a recent decision by the City Council. If the reporter stops adults on the street at random, what is the probability that it will take no more than three people to find a Democrat?

0.936

500

A jar has 250 marbles in it, 40 of which are red. What is the largest sample we can take (w/o replacement) if we want to use the binomial distribution to model the number of red marbles in our sample?

25

500

Tell how to find the variance of a distribution. You may give the formula, or tell how to find it on your calculator.

(x1-mean)2p1 + (x2-mean)2p2 + ... + (xi-mean)2pi

OR

Enter lists and run 1-Var Stats with L2 as the frequency, then square the standard deviation.

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