AP Statistics : Normal Distribution
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Example Questions
Example Question #1 : How To Use Tables Of Normal Distribution
Find the area under the standard normal curve between Z=1.5 and Z=2.4.
0.3220
0.0822
0.9000
0.0768
.0586
.0586
Example Question #1 : Normal Distribution
Alex took a test in physics and scored a 35. The class average was 27 and the standard deviation was 5.
Noah took a chemistry test and scored an 82. The class average was 70 and the standard deviation was 8.
Show that Alex had the better performance by calculating -
1) Alex's standard normal percentile and
2) Noah's standard normal percentile
Alex = .778
Noah = .723
Alex = .901
Noah = .926
Alex = .945
Noah = .933
Alex = .855
Noah = .844
Alex = .923
Noah = .911
Alex = .945
Noah = .933
Alex -
Noah -
Example Question #2 : How To Use Tables Of Normal Distribution
When
and
Find
.68
.76
.81
.61
.72
.72
Example Question #2 : Normal Distribution
Arrivals to a bed and breakfast follow a Poisson process. The expected number of arrivals each week is 4. What is the probability that there are exactly 3 arrivals over the course of one week?
Example Question #1 : How To Use Tables Of Normal Distribution
The masses of tomatoes are normally distributed with a mean of 
The Z score for a normal distribution at the 
Example Question #2 : Normal Distribution
Find
First, we use our normal distribution table to find a p-value for a z-score greater than 0.50.
Our table tells us the probability is approximately,
Next we use our normal distribution table to find a p-value for a z-score greater than 1.23.
Our table tells us the probability is approximately,
We then subtract the probability of z being greater than 0.50 from the probability of z being less than 1.23 to give us our answer of,
Example Question #3 : Normal Distribution
Find
First, we use the table to look up a p-value for z > -1.22.
This gives us a p-value of,
Next, we use the table to look up a p-value for z > 1.59.
This gives us a p-value of,
Finally we subtract the probability of z being greater than -1.22 from the probability of z being less than 1.59 to arrive at our answer of,
Example Question #3 : Normal Distribution
Gabbie earned a score of 940 on a national achievement test. The mean test score was 850 with a sample standard deviation of 100. What proportion of students had a higher score than Gabbie? (Assume that test scores are normally distributed.)
When we get this type of problem, first we need to calculate a z-score that we can use in our table.
To do that, we use our z-score formula:
where,
Plugging into the equation we get:
We then use our table to look up a p-value for z > 0.9. Since we want to calculate the probability of students who earned a higher score than Gabbie we need to subtract the P(z<0.9) to get our answer.
Example Question #3 : Normal Distribution
Which parameters define the normal distribution?
The two main parameters of the normal distribution are 
Example Question #1 : How To Identify Characteristics Of A Normal Distribution
All normal distributions can be described by two parameters: the mean and the variance. Which parameter determines the location of the distribution on the real number line?
Standard Deviation
Both
Mean
Variance
Mean
The mean determines where the normal distribution lies on the real number line, while the variance determines the spread of the distribution.
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