Show:
Catching Z's
Z Marks the Spot
Marbles
The Real World
Probabilities
Sampling Distributions
100
This tells us how many standard deviations above or below the mean a data value is.
What is a z-score?
100
If the population mean is 30 and the population standard deviation is 7.5, change 42 into a z-score.
What is 1.6
100
There are 7 pink and 8 blue marbles in a bag. Find the probability of choosing a pink and then a blue marble (with replacement).
What is 

56/225=0.2489?

100
Suppose the prices of a certain guitar are normally distributed with a mean of $159. What proportion of buyers would pay less than $150 if the standard deviation is $15?
What is .2743?
100
A correct interpretation of the statement, "the probability that a fair coin lands heads up is 0.50," is:


(A) To make sure that you get two heads you need to only flip four coins.

(B) In the next two flips of a coin, there will be exactly one head and one tail.

(C) A computer simulation of 100 coin flips would produce exactly 50 heads and 50 tails.

(D) Over a long period of time, there will be equal proportions of heads and tails.

What is D? (this is the Law of Large Numbers)
100

This law explains:

*that as the sample size increases, the sample mean is more likely to be close to the population mean

*larger sample size will result in less sampling error.



What is the law of large numbers?

200
Using z scores (or the z table) is appropriate for data with this shape.
What is normal or bell-shaped?
200
IQ scores are normally distributed with a mean of 97 and a standard deviation of 11. An individual's IQ score is 110. Find the z-score corresponding to this value.
What is z=1.18?
200
A bag of 10 marbles has 5 green marbles, 3 blue marbles, and 2 yellow marbles.


Find the probability of selecting 2 blue marbles if the first selection is replaced before the next selection is made.

What is 

9/100=0.09?

200
The length of time people wait to ride a roller coaster is normally distributed with a mean time of 20 minutes and a SD of 6 minutes. Find the probability that you will wait more than 30 minutes for the ride.
What is .0478?
200
There is a 13/52 chance of a person drawing a spade from a normal deck of cards. 


Find the probability of a person drawing another spade given that the first card was not put back into the deck.

What is 

12/51=0.2353?

200
Scores on a measure of science knowledge are skewed right with a mean of 85 and a standard deviation of 10. A researcher wants to conduct a study with 90 people from the population. What is the shape of the distribution of the sample means?
What is bell-shaped (or normal)?
300
Find the area under the standard normal curve to the left of z=-1.23.
What is 0.1093?
300
Find the z-score for which 20% of the area lies to the left.
What is -0.84 ?
300
A bag of 10 marbles has 5 green marbles, 3 blue marbles, and 2 yellow marbles.


Find the probability of selecting a green marble followed by a yellow marble if each selection is not replaced.

What is 

10/90=0.1111?

300
The number of cars that go through the drive thru at Wendy's in a day is normally distributed with a mean of 120 and a SD of 30. What is the probability that more than 170 cars go through the drive-thru today?
What is .0478?
300
There is a 4/52 chance of drawing a queen from a normal deck of cards. There is a 1/52 chance of drawing a queen of diamonds.


Find the probability of drawing a diamond card given that the card drawn was a queen.

What is 

1/4=0.25?

300

Which is more variable? 

(A) the distribution of the sample means with this larger sample size (N=25)

(B) the distribution of sample means when the sample size was smaller (N=5)?

What is B?
400
Find the area under the standard normal curve to the right of z=1.75.
What is 0.0401?
400
Find the z-score for which 10% of the data lies to the right.
What is 1.28 ?
400
There are 35 yellow and 17 purple marbles in a bag.  


Find the probability of choosing a purple and then a yellow marble (with replacement).

What is 

595/2704=0.2200?

400
The amount of coffee a machine dispenses is normally distributed with a mean of 11.8 oz and a standard deviation of .25 oz. When the machine dispenses more than 12.5 oz the cup must be refilled. What is the probability that a cup is refilled?
What is .0026?
400
There is a 13/52 chance of a person drawing a club from a normal deck of cards. 


Find the probability of a person drawing a king given that it is a club.

What is 

1/13=0.0769?

400

As the variability in the distribution of sample means decreases, the amount of sampling error:

(A) stays the same  

(B) increases   

(C) decreases

What is C? 

500
Find the area under the standard normal curve between z=1.05 and z=2.24.
What is 0.1343?
500
If the z-score for x=28 is -0.5 and the population standard deviation is 8, find the population mean.
What is 32?
500

A bag of 10 marbles has 5 green marbles, 3 blue marbles, and 2 yellow marbles. 


Find the probability of selecting all blue marbles if each selection is not replaced.

What is 

6/720=0.0083?

500
The amount of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight distribution?
What is 48.59 ounces?
500
Two events A and B are mutually exclusive. 


P(A)=0.4 and P(A or B)=0.6. Find P(B).

What is 0.2?
500

What is the expected amount of sampling error between the sample mean of a given size and the population mean?


What is 

sigma/sqrt(n)?