Download Homework 8

Homework 8
Problems 1-5 are adapted from problems 3,4, 15, 16, and, 22 from Chapter 17 of the book.
Problems 6 and 7 are adapted from worksheets by Karla Karstens.
1. Consider the normal distribution below. P 0 and P represent values one standard
deviation away from the mean.
(a) Find the mean of the distribution.
(b) Find the standard deviation of the distribution.
2. Consider the normal distribution below. P 0 and P represent values one standard
deviation away from the mean.
(a) Find the mean of the distribution.
(b) Find the standard deviation of the distribution.
3. A normal distribution has mean µ = 30 kg and standard deviation σ = 15 kg. Find
the z-value of the each of the following:
(a) x = 45 kg
(b) x = 0 kg
(c) x = 54 kg
(d) x = 3 kg
Math 017 A - Applications of Finite Math
Fall 2015
Homework 8
4. A normal distribution has mean µ = 110 points and standard deviation σ = 12 points.
Find the z-value of each of the following:
(a) x = 98 points
(b) x = 110 points
(c) x = 128 points
(d) x = 71 points
5. In a normal distribution with mean µ = 83.2 and standard deviation σ = 4.6, find the
data value corresponding to each of the following z-values:
(a) z = 2
(b) z = −1.5
(c) z = −0.43
(d) z = 0
6. The Waterman Manor Coffee machine dispenses 8 ounces of coffee in 9 ounce cups.
Machines are never perfect, so sometimes it actually dispenses a bit less than 8 ounces
or a bit more than 8 ounces. Assume the actual amount dispensed has an approximately
normal distribution with mean µ = 8 ounces and standard deviation σ = 0.3 ounces.
(a) What are the chances that the cup of coffee is between 7.7 ounces and 8.3 ounces?
(b) What are the chances that the cup of coffee is between 7.4 ounces and 8.6 ounces?
(c) What are the chances that the cup of coffee is between 7.1 ounces and 8.9 ounces?
(d) What are the chances that the cup of cofee is more than 8 ounces?
(e) What are the chances that the cup of cofee is less than 8 ounces?
(f) What are the chances that the cup of coffee is between 8 ounces and 8.6 ounces?
(g) What are the chances that the cup of coffee is between 7.7 ounces and 8 ounces?
(h) What are the chances that the cup of coffee is between 7.1 ounces and 8.3 ounces?
(i) What are the chances that the cup of coffee is between 8.3 ounces and 8.9 ounces?
(j) What are the chances that the cup of coffee is between 7.4 ounces and 7.7 ounces?
(k) What are the chances that the cup of coffee is less than 8.6 ounces?
(l) What are the chances that the cup of coffee is more than 7.1 ounces?
(m) What are the chances that the cup of coffee is less than 7.4 ounces?
(n) What are the chances that the cup of coffee is more than 8.9 ounces?
Math 017 A - Applications of Finite Math
Fall 2015
Homework 8
7. A psychology class runs a memory study. Participants are given two minutes to study
a set of objects on a tray and then see how many they can recall after two minutes.
The number of objects recalled approximates a normal distribution with mean µ = 20
objects recalled, and standard deviation σ = 3 objects. Use the 68-95-99.7 empirical
rule to answer each of the following.
(a) Approximately what percent of the particpants recalled between 17 and 23 objects?
(b) Approximately what percent of the of participants recalle dbetween 14 and 26
objects?
(c) Approximately what percent of the participants recalled less than 23 objects?
(d) Approximately what percent of the participants recalled less than 14 objects?
(e) Approximately what percent of the participants recalled between 14 and 20 objects?
(f) Approximately what percent of the participants recalled between 17 and 26 objects?
(g) Approximately what percent of the participants recalled between 23 and 26 objects?
Math 017 A - Applications of Finite Math
Fall 2015