Unit 6

Question 1

What 2 things must you have been given in a question to know you have a binomial distribution?

Answer 1

• n and p.`

Question 2

What do all binomial distributions have?

Answer 2

• Only two possible results: yes or no.
• Must know the sample size, or number of trials given (n).
• Must know the probability of the number of “yeses” (p)

Question 3

Sample size =

Answer 3

s

Question 4

Probability of a yes =

Answer 4

p

Question 5

The number of yeses =

Answer 5

x

Question 6

Examples of binomial distributions:

Answer 6

• “You are rolling a fair die”
• “You are tossing a fair coin”
• “You are guessing on a test”

Question 7

What given formula do you use for binomial distributions?

Answer 7

n choose k.

Question 8

How can we tell if the random variable X has an approximately normal distribution?

Answer 8

If np is greater or equal to 10, and if n(1-p) is greater than 10.

Question 9

What can we do if we know X has an approximately normal distribution?

Answer 9

We can change x-scores into z-scores using table A.

Question 10

How do you calculate mean of x in a binomial distribution?

Answer 10

np

Question 11

How do you calculate standard deviation of x in a binomial distribution?

Answer 11

square root of np(1-p)

Question 12

How to solve a binomial probability using the normal approximation:

Answer 12

• Find mean (np) and s.d. (square root of np(1-p))
• Draw an x-bell curve entered at the mean and shade the region of interest (The x-values boxed in your sample space)
• Use a standardizing formula to get z (z=x-mean/s.d)
• Use table A to find the probability.

Question 13

When estimating a SAMPLE proportion, we use p hat, what is the formula to get p hat?
ie. “a random sample of 1000 dentists found 330 use crews toothpaste”

Answer 13

p hat = x/n

Question 14

As sample size (n) gets larger, the distribution of p hat becomes __________.

Answer 14

More and more bell shaped.

Question 15

What is the law of large numbers?

Answer 15

The spread of distribution gets narrower as n gets larger.

Question 16

Formula for standardizing p hat into a z-score * given *:

Answer 16

Formula 5:

z = p hat - p / square root of p(1-p)/n