MAT 205 Wilmington University Statistics Questions

Link that’s on page 1. if needed

World’s Most Polluted Countries in 2020 – PM2.5 Ranking | AirVisual (iqair.com)

1. The chart below shows some pollution indexes for some of the world’s countries.
Answer the questions Show your calculations. (See page 432)
2020 World Air Quality Report
a.
Which country was in the 70-
percentile position?
b. What was the percentile for
Belgium?
Country
New Caledonia
Estonia
Australia
Belgium
Denmark
Spain
Latvia
Philippines
Hungary
Hong Kong SAR
Albania
Peru
Mexico
Kosovo
Croatia
Laos
Montenegro
United Arab Emirates
Kuwait
Bosnia Herzegovina
Afghanistan
PM2.5
3.7
5.9
7.6
8.9
9.4
10.4
11.3
12.8
14.3
15.4
16.0
17.9
18.9
20.0
21.2
22.4
26.1
29.2
34.0
40.6
46.5
C.How many countries were the best 20% for
air quality (smallest PM2.5)?
d. of the countries in the list, name the
countries that are in the 10% which pollute
the least.
https://www.iqair.com/us/world-most-
polluted-countries
2. For the data from question 1, find the quartiles, the interquartile range, and draw a box
plot. (See pages 437-439) Be sure to have a even scale for your box plot.
Minimum
Interquartile Range
Low Quartile Q1
Median Q2
Upper quartile Q3
Maximum
3. Use the Empirical Rule (page 454) to answer the following questions. A standardized
test of intelligence is scaled so that the mean IQ is 100, and the standard deviation is 15.
a. What percent of people have an IQ between 85 and 115?
b. What percent of people have an IQ greater than 115?
c. What percent of people have an IQ less than 130?
d. What percent of people have an IQ less than 70?
4. Use Z-scores to solve the following question.
In math class, Samantha scored 10 on a quiz for which the class mean was 7.6 and the class
standard deviation was 2.1. Marie scored 8.5 on a quiz for which the class mean was 5.9 and
the class standard deviation was 2.1. Relatively speaking, who had the better score? What
was each of their z-scores? (See page 458)
5. Using technology or the table on page 471, find the following probabilities. Tell what
method you used.
a. Between -1.10 and 0.47
b. To the left of 1.05
C. To the right of 2.38
Extra credit
A fruit-packing company produced peaches last summer whose weights were normally
distributed with a mean 14 ounces and standard deviation 0.6 ounces. Among a sample of
1000 of those peaches, about how many could be expected to have weights as follows?
a. At least 14 ounces
b. Between 14 and 15.2 ounces
C. Less than 13.4 ounces
d. More than 12 ounces