Download Common Core Math III Unit 1: STATISTICS!

Z-Score Practice
1) Apples have an average weight of 150g, and a standard
deviation of 10g. Oranges have an average weight of
140g, and a standard deviation of 7g.
a) Juan’s Apple is 168g and Natalie’s orange is 157g.
Respective to their fruits, whose fruit is bigger?
b) Yasmin has a really big apple that is 3.2 standard
deviations above the mean. What is the weight of his
apple?
c) Draw a Normal Curve for Oranges.
d) What is the percentage of having an orange that
weights between 126g and 147g?
e) What is the percentage of a having an orange greater
than 154g?
Common Core Math III
Unit 1: Statistics
We will discuss the following four
topics during this unit:
1. Normal Distributions
2. Sampling and Study Design
3. Estimating Population Parameters
4. Expected Value and Fair Game
Objectives
1) Review z-scores and empirical
rule
2) Use technology to calculate
probabilities in a normal
distribution
Lets look at the same example from
yesterday.
The scores on the CCM3 midterm were
normally distributed. The mean is 82 with
a standard deviation of 5. Create and label
a normal distribution curve to model the
scenario.
You might be wondering…
what happens if you’re looking
for scores that are not perfect
standard deviations away from
the mean?
normalcdf (lower bound,
upper bound, µ, σ)
a. What’s the probability that a randomly
selected student scored between 80 and 90?
normalcdf (80, 90, 82, 5) = 0.6006
b. What’s the probability that a randomly
selected student scored below 70?
normalcdf (0, 70, 82, 5) = 0.0082
c. What’s the probability that a randomly
selected student scored above 79?
normalcdf (79, 100, 82, 5) = 0.7256
You can also work backward to find percentiles!
d. What score would
a student need in
order to be in the 90th
percentile?
invnorm (percent of area to left, , )
invnorm (0.9, 82, 5) = 88.41, or 89
e. What score would a student need in order
to be in top 20% of the class?
invnorm (0.8, 82, 5) = 86.21, or 87
The average waiting time at Walgreen’s drivethrough window is 7.6 minutes, with a
standard deviation of 2.6 minutes. When a
customer arrives at Walgreen’s, find the
probability that he will have to wait
a. between 4 and 6 minutes 0.186
b. less than 3 minutes 0.037
c. more than 8 minutes 0.439
d. Only 8% of customers have to wait longer
than Mrs. Jones. Determine how long Mrs.
Jones has to wait. 11.25 minutes
Warm Up 8/28
The average IQ is 99, with a standard deviation of
15.
a) Draw a Normal Curve
b) What percent of people have a higher IQ than
129?
c) What percent of people have an IQ between 54
and 99?
d) What percent of people have an IQ between 70
and 115?
e) What IQ do you need to be in the top 15% of
people?
Warm Up
8/27
The average calories intake for our class is 2,200
calories with a standard deviation of 300 calories.
a) Construct a Normal Curve.
b) What percent of students fall between 1900 and
3100 calories per day?
c) What percent of student fall between 1880 and
2600
d) If Mia was in a rush and skipped breakfast one
day, and her calories intake was only 1400, how
many standard deviations away is she from the
mean (z-score)?
Questions
about normal
distribution?