Download Review Continuous Distributions Test Continuous Distributions: you

Review Continuous Distributions
Test Continuous Distributions: you should be able to
1. Calculate proportions/probabilities of density curves (unusual density curves and uniform density
curves).
2. Find proportions/probabilities using the Empirical Rule for a Normal Distribution.
3. Draw and appropriately label the Normal model (including the Empirical Rule).
4. Use standard observations (z-scores) on a Normal distribution to find proportions/probabilities.
5. Interpret probabilities and find values on a Normal distribution given the area under the curve.
These concepts are from notes on density curves and Chapter 6 of the textbook. Please make sure you
understand how to do all the problems from your two quizzes (Continuous distribution density curves
and continuous distribution normal model). Additional problems to look at are from 5 Steps to a 5 AP
Statistics 2014, 2015 by Duane C. Hinders.
5 Steps to a 5: pg. 160
4.
The GPAs (grade point averages) of student who take the AP Statistics exam are approximately
normally distributes with a mean of 3.4 and a standard deviation of 0.3. Using Table A, what is the
probability that a student selected at random from the group has a GPA lower than 3.0.
a. 0.0918
b. 0.4082
c. 0.9082
d. -0.0918
e. 0
6.
The student in problem #4 above were normally distributed with a mean GPA of 3.4 and a
standard deviation of 0.3. In order to qualify for the school honor society, a student must have a GPA in
the top 5% of all GPA’s. Accurate to two decimal places, what is the minimum GPA Norma must have in
order to qualify for the honor society?
a. 3.95
b. 3.92
c. 3.75
d. 3.85
e. 3.89
Pg. 163
7. Which of the following statement is (are) true of a normal distribution?
I.
Exactly 95% of the data are within two standard deviations of the mean.
II.
The mean = the median = the mode.
III.
The area under the normal curve between z = 1 and z = 2 is greater than the area between z = 2
and z = 3.
9. A normal distribution has mean 700 and standard deviation 50. The probability is 0.6 that a randomly
selected term from this distribution is above x. What is x?
11. Consider a probability density curve defined by the line y = 2x on the interval [0, 1] (the area under
y = 2x on [0, 1] is 1). Find P(0.2< x < 0.7)
12. Half Moon Bay, California, has an annual pumpkin festival at Halloween. A prime attraction to this
festival is a “largest pumpkin” contest. Suppose that the weights of these giant pumpkins are
approximately normally distributed with a mean of 125 pounds and a standard deviation of 18 pounds.
Farmer Harv brings a pumpkin that is at the 90th percentile of all the pumpkins in the contest. What is
the approximate weight of Harv’s pumpkin?
20. The normal random variable X has a standard deviation of 12. We also know that P(x > 50) = 0.90.
Find the mean of the distribution.