Name _______________________________
Period ___________________
Special Topics Homework
Section 8.4 Day 1
1.
If a density curve has a uniform distribution over the interval from 2 to 15, what value, on the y-axis,
would mark the height of this density curve? Draw the curve and mark it correctly. Then answer the
questions which follow.
a) What is the probability picking a number and having it be between 4 and 9?
b) What is the probability of picking a number less than 5?
c) What is the probability of picking a number that is at least 10? Greater than 15?
2.
Refer to the irregular curve given below and answer the questions which follow.
Given the following curve:
0.1
0.05
20
40
a)
Verify that the total area under the curve is equal to 1 (that it is a valid density curve).
b)
What percent of observations occur when x  20 ? When x  20 ?
c)
What percent of observations occur when x  10 ? when x  30 ?
d)
What percent of observations occur when 10  x  30 ?
3.
A certain density curve consists of a straight-line segment that begins at the origin (0,0) and has a
slope of 1.
4.
a)
Sketch the density curve. What is the right endpoint of the line segment?
d)
What percent of the observations lie below 0.5? above 1.5?
Refer to the uniform curve given below and answer the questions which follow.
.5
0
1
2
a)
Verify mathematically that it is a density curve.
b)
Is the mean of the x-values equal to the median?
c)
Calculate the probability of the range of values which make up the inter-quartile range.
d)
What is the probability of an x-value being greater than or equal to .5? Less than .5?