Lab 10 Spring 2016
Exam 2 Review
1. Assume that z scores are normally distributed with a mean of 0 and a standard
deviation of 1. If P(O < z <a)= 0.3577, find a.
2. Assume that z scores are normally distributed with a mean of 0 and a standard
deviation of
STAT212
Practice Questions for Exam 2
1. An investigator claims that = the average weight of passengers flying on small planes exceeds the FAA guideline of
average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppo
STAT212
Exam 2 Summer 2015
Name_
Multiple-Choice Part: Each multiple-choice question is worth 2 points.
1. Which of the following would be an appropriate alternative (research) hypothesis?
A) The mean of a population is less than 55.
B) The mean of a sam
ConceptsforExam2
*This list is meant to help guide your studying. It may NOT be an exhaustive list.*
Normal Distribution (more in context with distribution of sample mean and sample proportion)
Be able to calculate probabilities for a normal random varia
Class examples Probability of events, and additive rules (Sect. 2.4-2.5)
1. The probabilities that a car mechanic will service 3, 4, 5, 6, 7, or 8 or more cars on any given workday are 0.12,
0.19, 0.28, 0.24, 0.10 and 0.07, respectively. What is the proba
WASHINGTON STATE
g: UNIVERSITY
/ VANCOUVER
Probability and Statistics
STAT 360, Fall 2016
Class examples Introduction to Statistics and Data Analysis
1. The following is data associated with a study conducted at Virginia Polytechnic Institute and State
Class examples (Sect. 3.3)
1. Let T represent the time until failure (in years) of a randomly selected component. We believe that T has density
function f (t) = 0.5 e0.5t, t 0.
(a) Verify that f (t) is indeed a density function.
(b) What is the cumulative
Class examples Conditional probability, independence, and the product rule (Sect. 2.6)
1. In a city, 60% of all households get Internet, 80% get cable, and 50% get both services. If a household gets at
least one of these services:
(a) what is the probabil
Class examples Counting sample points (Sect. 2.3)
1. An employee from Washington state can choose among three group life insurance plans and five group health
insurance plans. If the employee chooses one life insurance plan and one health insurance plan,
Binomial and Multinomial Distributions
October 20, 2016
Bernoulli Trials
An experiment with only two possible outcomes, typically denoted success and failure.
If P (success)=p, then the P (f ailure) is 1 p (sometimes denoted q).
Note that success does not
Class examples (Sect. 3.1-3.2)
1. Specify if the random variables representing the following are discrete or continuous:
(a) The lifetime of a device:
(b) Number of students in a random class:
(c) Number of trains arriving to a station:
(d) Time until the
Class examples (Sect. 4.1)
1. The number of interviews that a student has prior to getting a job is represented by the random variable X with
36
probability function () = 49 2, for x = 1,2,3. Find the expected number of interviews prior to getting a job.
Normal Probabilities
Common Data
Mean
Standard Deviation
7
6
Probability for X <=
X Value
Z Value
P(X<=7)
7
0
0.5000
Probability for X >
X Value
Z Value
P(X>9)
9
0.33333333
0.3694
Probability for X<7 or X >9
P(X<7 or X >9)
0.8694
Probability for a Range
F
Paired t Test
Data
Hypothesized Mean Diff.
Level of Significance
0
0.05
Intermediate Calculations
Sample Size
DBar
degrees of freedom
SD
Standard Error
t Test Statistic
Two-Tailed Test
Lower Critical Value
Upper Critical Value
p-Value
Reject the null hypo
"Dow Dogs" Population
Parameters
1Yr-Return
Mean
7.6570
Variance
84.8352
Standard Deviation
9.2106
"Dow Dogs" Population
Parameters
1Yr-Return
Mean
7.6570
Variance
84.8352
Standard Deviation
9.2106
Stock
AT&T
Verizon
Merck
Pfizer
GE
DuPont
Johnson & Johns
For the Mean Sales Invoice Amount
Data
Population Standard Deviation
Sampling Error
Confidence Level
Intemediate Calculations
Z Value
Calculated Sample Size
25
5
95%
-1.9600
96.0365
Result
Sample Size Needed
97
For the Mean Sales Invoice Amount
Data
Popul
For the Proportion of In-Error Sales Invoices
Data
Estimate of True Proportion
Sampling Error
Confidence Level
Intermediate Calculations
Z Value
Calculated Sample Size
0.15
0.07
95%
-1.9600
99.9563
Result
Sample Size Needed
100
For the Proportion of In-Er
t Test for the Hypothesis of the Mean
Data
Null Hypothesis
m=
Level of Significance
Sample Size
Sample Mean
Sample Standard Deviation
Intermediate Calculations
Standard Error of the Mean
Degrees of Freedom
t Test Statistic
120
0.05
12
112.85
20.8
6.0044
1
Variability in a Distribution
Data
Mean
Standard Deviation
2.06
0.02
Results
1 standard deviations
2 standard deviations
3 standard deviations
% of Values Found in Intervals Around the Mean
Range
2.04
2.02
2.00
2.08
2.10
2.12
Chebyshev Rule (any
distribut
Z Test for the Mean
Data
Null Hypothesis
m =
Level of Significance
Population Standard Deviation
Sample Size
Sample Mean
Intermediate Calculations
Standard Error of the Mean
Z Test Statistic
368
0.05
15
25
372.5
3
1.5
Two-Tail Test
Lower Critical Value
-1
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
Level of Significance
Group 1
Number of Successes
Sample Size
Group 2
Number of Successes
Sample Size
Intermediate Calculations
Group 1 Proportion
Group 2 Proportion
Difference in Two
Z Test of Hypothesis for the Proportion
Data
Null Hypothesis
p=
Level of Significance
Number of Items of Interest
Sample Size
Intermediate Calculations
Sample Proportion
Standard Error
Z Test Statistic
0.3
0.05
320
1000
0.3200
0.0145
1.3801
Two-Tail Test
Math/Stat 370
Fall 2015
Homework 1 Solution
1.
9
a.
Sample average:
x
x
i
i 1
n
9
x
i
26.79
2.679
10
9
x
26.69
2
i
i 1
Sample standard devation:
s
mm
7.48535
i 1
7.48535
26.692
10
10 1
0.3425656 0.585291
b. When each value is divided by 10,
is reduc
Math/Stat 370
Exam 3 Fall 2013 (80 pts)
Name _
ID Number _
Part I. Workout Problems. Show calculations in support of your answers. Unsupported answers will not receive
full credit. (48 points)
1.
The target fill weight for a box of cereal is 350 g. In eac
Math/Stat 370
Exam 2 Fall 2013 (80 pts)
Name _
ID Number _
Part I. Workout Problems. Answers with no supporting solution will NOT receive full credit. [48 pts]
1.
Data on proportional stress limits (in MPa) for specimens made from 2 different types of woo