Friday, November 18th.
Chapter 16 Worksheet (Day 2)
Work these problems in your homework notebook.
1) The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” suggests
the uniform distribution on the interval 7.5 to 20 as a model for x= depth (cm) of the bioturbation layer in
sediment for a certain layer ( Please don’t ask me what the bioturbation layer is!).
(a) Draw a density curve.
(b) What is the probability that x is at most 12?
(c) What is the probability that x is between 10 and 15?
2) Let x= the amount of gravel sales (tons) during a randomly selected week at a particular sales facility.
Suppose that the density curve has height f(x) above the value x, where
2(1  x) where 0  x  1
f ( x)  
otherwise
 0
(a) Draw the curve
1

(b) Find P  x   =
2

1

(c) Find P  x   =
2

1
1
(d) Find P   x   =
2
4
3) A personal computer salesperson working on a commission receives a fixed amount for each system
sold. Suppose that for a given month, the probability distribution of x= the number of systems sold is given
below:
X
1
2
3
4
5
6
7
8
P(X)
.05
.10
.12
.30
.30
.11
.01
.01
(a) Find the mean number of systems sold. How would you interpret this value?
(b) Find the variance and standard deviation of x. How would you interpret these values?
(c) What is the probability that the number of systems sold is within 1 standard deviation of its mean
value?
(d) What is the probability that the number of systems sold is more than 2 standard deviations from the
mean value?
4) An express mail service charges a special rate for any package that weighs less than 1 pound. Let x= the
weight of a randomly selected parcel that qualifies for this special rate.
.5  x where 0  x  1
f ( x)  
otherwise
 0
(a) Sketch the graph of the density curve.
(b) What is the probability that a randomly selected package of this type is at most one-half of a pound?
(c) What is the probability that a randomly selected package of this type is between one-fourth and onehalf of a pound?
(d) What is the probability that a randomly selected package of this type is at least three-fourths of a
pound?
7
11
and  x2 
(e) Suppose it is known that  x 
12
144
What is the probability that the value of x is more than 1 standard deviation from the mean value?