Download Unit 3 Review Guide

Statistical Reasoning
Unit 3 Review
What you need
to know & be
able to do
MSRAD1.a.i-ii.
Describe and
interpret the
shape of the
distribution
Name:_______________________________
Date:_____________________ Period:_____
Things to remember
Examples
-On a skewed distribution, the mean is pulled by the
skew.
-Median always divides the area of a curve in half.
1. Using the curve below, which segment represents the median?
Not all data is normally distributed.
3. Which of the following are most likely to have a skewed distribution?
2. Using the curve below, which segment represents the mean?
Describe and
interpret the
measures of
center for the
distribution.
MSRAD1.a.iii.
Describe and
interpret the
patterns in
variability for the
distribution.
Normal Distribution/Normal curve
a. IQ scores of all students at Princeton.
b. The ACT English scores of all Freshmen entering KSU this Fall.
c. NBA players’ incomes.
d. Gestation period of rhinoceros.
e. Heights of all 20 year old females in New York.
f. Prices of homes in a neighborhood.
A Normal distribution has a mean of 25 and a standard deviation of 5.
Find the area under the curve for the following intervals:
4. Between 20 and 30
5. At least 20
The standard Normal curve has z-scores on the x-axis
with mean 0 and standard deviation of 1.
6. At most 30
7. Less than 15 or more than 35
MSRIR1
Use z-scores to
calculate
percentiles and
areas under a
Normal
distribution.
z
x X

A Normal distribution has a mean of 112.8 and a standard deviation of
9.3. Use the standard normal table to find the area covered by the
following intervals:
8. x ≤ 104.3
9. x ≥ 79.6
10. x is between 106.2 and 127.1
Use the table given in class and the value of z to find the percentile.
11. z = -1.78
12. z = 2.62
13. z = 0.34
14. Scores on the SAT follow a normal distribution with mean 452 and
standard deviation 18. Michael’s z-score is 1.34; what is his actual SAT
score?
15. What is the meaning of a z-score of -1?
16. A z-score of 2.5 is equivalent to what percentile?
The histogram below shows how many calories a group of 300 women are
eating in their morning snack.
17. What percentile is 136 calories? How many women is that?
18. Interpret this percentile in context of this problem.
A county is having a bottle recycling competition between homerooms in
high schools around the county. The histogram below shows the
percentage of homerooms that collected the amount of bottles collected in
hundreds.
19. What percentile is 500 bottles?
20. Interpret this percentile in context of this problem.
22. If there are 1200 homerooms in high schools around this particular
county, how many collected less than 700 bottles?
MSRAD1.a.i-ii.
Describe and
interpret the
shape of the
distribution
Describe and
interpret the
measures of
center for the
distribution.
Uniform Distributions
23. A computer’s random number generator is designed to produce
numbers between 1 and 5, with equal likelihood that the number produced
will fall at any point within this interval.
(a) Sketch a density curve that illustrates this situation. Make sure to label
each axis correctly. (Recall that the total area under the density curve
must be 1.)
(b) What percent of the random numbers generated fall between 2 and 4?
Show your work.
(c) What proportion of the random numbers generated fall above 2?
Show your work.
24. The amount of time that a person must wait for a metro to arrive at its
station is uniformly distributed between 0 and 8 minutes.
(a) Draw a density curve to represent this situation (don’t forget to include
the appropriate height):
(b) What is the probability that a person must wait 6 or fewer minutes for
the metro?
(c) On average, how long must a person wait for the metro?
(d) 80% of the time, the time a person must wait for the metro falls below
what value? (In other words, what is the 80th percentile?)