MATH 107NAME:_______________________
EXAM 2
Show all work for credit and keep answers exact when possible.

1. Classify the following statement as an example of classical, empirical, or subjective probability and explain your reasoning. According to your doctor he feels the chance of you surviving a surgery is 0.85.

Subjective; based upon his feelings.

2. Determine the two events described in the study. Do the results indicate that the events are independent or dependant? Researchers found that people with depression are five times more likely to have a breathing- related sleep disorder than people who are not depressed.

Depression and Breathing-related sleep disorders; Dependant

3. A horse race has 10 entries. Assuming that there are no ties, what is the probability that the three horses owned by one person finish first second, and third? The number of possible combinations of 3 horses winning, in any order, is

So the probability is

4. In how many distinguishable ways can the letters in the word statistics be written?

5. The table shows the results of a survey that asked 2850 people whether they are involved in any type of charity work. | Frequently| Occasionally| Not at all| Total|
Male| 221| 456| 795| 1472|
Female| 207| 430| 741| 1378|
Total| 428| 886| 1536| 2850|

A person is selected at random from the sample.

a) What is the probability the person is female or occasionally involved in charity work?

b) Are the events “being female and occasionally involved in charity work” and “being frequently involved in charity work” mutually exclusive? yes

6. A company gave psychological tests to perspective employees. The random variable x represents the possible test scores.

a) Use the histogram to find the probability that a person selected at random from the survey’s sample had a test score of more than two.

...milligrams of tar per cigarette and a standarddeviation equal to 1.0 milligram. Suppose a sample of 100 low-tar cigarettes is randomly selected from a day’s production and the tar content is measured in each. Assuming that the tobacco company’s claim is true, what is the probability that the mean tar content of the sample is greater than 4.15 milligrams?
[0.00621]
2. The safety limit of a crane is known to be 32 tons. The mean weight and thestandarddeviation of a large number of iron rods are 0.3 ton and 0.2 ton respectively. One hundred rods are lifted at a time. Compute the probability of an accident.
[0.1587]
3. A soft –drink vending machine is set so that the amount of drink dispensed is a randomvariable with a mean of 200 milliliters and a standarddeviation of 15 milliliters. What is the probability that the mean amount dispensed in a random sample of size 36 is at least 204 milliliters?
[0.0548]
4. An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean (μ) = 117 cm and standarddeviation (σ) = 6.1 cm. Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120 cm.
[0.16354]
5. The number of pizzas consumed per...

...I'll be honest. Standarddeviation is a more difficult concept than the others we've covered. And unless you are writing for a specialized, professional audience, you'll probably never use the words "standarddeviation" in a story. But that doesn't mean you should ignore this concept.
The standarddeviation is kind of the "mean of the mean," and often can help you find the story behind the data. To understand this concept, it can help to learn about what statisticians call normal distribution of data.
A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other.
Let's say you are writing a story about nutrition. You need to look at people's typical daily calorie consumption. Like most data, the numbers for people's typical consumption probably will turn out to be normally distributed. That is, for most people, their consumption will be close to the mean, while fewer people eat a lot more or a lot less than the mean.
When you think about it, that's just common sense. Not that many people are getting by on a single serving of kelp and rice. Or on eight meals of steak and milkshakes. Most people lie somewhere in between.
If you looked at normally distributed data on a graph, it would look something like this:
The x-axis (the horizontal one) is the value in question......

...Deviation
Definition:
Behavior commonly seen in children that is the result of some obstacle to normal development such behavior may be commonly understand as negative (a timid child, a destructive child) or positive (a quite child), both positive and negative deviation will disappear once the child begins to concentrate on a piece of work freely chosen by him.
The physical deforms are easier to identify. This can be by birth due to an accident etc… and most such physical deforms can be either cured. However, deforms that take place in development of psychological aspects of a child are not only threat to building the character and the personality of the child also you find certain physical deforms in curable in medicine.
Dr. Montessori, according to her she fugues deviated children are.
The naughty children act and react very strong as a result of severe treatment they have received. So their behavior is cruel from others.
The weak children are always mistaken for good children and parent are happy because of their timidly and but they are lazy and afraid of everything.
The bright children are very imaginative and live in their own fantasy world.
Deviations shown by the strong and weak children are:
In the absorbent mind Montessori discussed deviation shown by the strong, meaning those who resist and overcome the obstacles they meet and deviation...

...StandardDeviation (continued)
L.O.: To find the mean and standarddeviation from a frequency table.
The formula for the standarddeviation of a set of data is [pic]
Recap question
A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box):
[pic].
Calculate the mean and standarddeviation for x.
Introductory example for finding the mean and standarddeviation for a table:
The table shows the number of children living in a sample of households:
|Number of children, x |Frequency, f |xf |x2f |
|0 |14 |0 × 14 = 0 |02 × 14 = 0 |
|1 |12 |1 × 12 = 12 | |
|2 |8 | | |
|3 |6 | |32 × 6 = 54 |
|TOTAL |[pic]...

...StandardDeviation
objective
• Describe standarddeviation and
it’s importance in biostatistics.
Measure of Dispersion
• Indicates how widely the scores
are dispersed around the central
point (or mean.)
-StandarddeviationStandardDeviation.
• The most commonly used method
of dispersion in oral hygiene.
• The larger the standarddeviation,
the wider the distribution curve.
StandardDeviation
• SD, , (sigma)
• Indicates how subjects differ from
the average of the group/ the more
they spread out, the larger the
deviation
• Based upon ALL scores, not just
high/low or middle half
• Analyzes descriptively the spread of
scores around the mean
– 14+ 2.51 = Mean of 14 and SD of
2.51
StandardDeviation
• The spread of scores around the
mean:
• For example, if the mean is 60 and
the standarddeviation 10, the
lowest score might be around 30,
and the highest score might be
around 90.
StandardDeviation &
Variance
Usefulness
• When comparing the amount of dispersion in
two data sets.
• Greater variance = greater dispersion
• Standarddeviation--”average” difference
between the mean of a sample and each data
value in the sample
14+ 2.51 = Mean of 14 and SD of 2.51
Distribution...

...etc) in Docsharing and using Excel, provide the following for the variable(s) of your choice:
1. Frequency distribution of a variable and bar graph of the same variable
2. Descriptive statistics of a continuous dataset: mean, median, mode, skewness, kurtosis, standarddeviation
3. Cross tabulation of two variables
4. Comparison of the effect of three or more groups (singlevariable) on a single continuous variable
5. Scatterplot of two continuous variables
6. Correlation between the two continuous variables
______________
HERE ARE MORE SPECIFIC DETAILS:
1. Frequency distribution bar graph (as in Week #1) – nominal or ordinal variables (Polit, p. 25)
2. Continuous variable descriptive stats: mean, median, mode, skewness, kurtosis, SD – (as in Week #1 Simple Descriptive Excel Worksheet) – requires a continuous variable, e.g., bp, wt, ht
3. Cross tabulation of two variables – requires making a table (as per Polit pp. 59-61) using nominal variables or groups, e.g., yes or no; on meds or not on meds; married or not married, etc. (Week #2)
4. Comparison of the effect of three or more groups (single variable) on a single continuous variable – this is a One-Way ANOVA with groups, e.g., ed status,...

...A survey is conducted in Chicago (population 2,800,000) using random-digit-dialing equipment which place calls at random to residential phones, both mobile and landline. The purpose of the survey is to determine the percentage of adults who would favor a half-cent increase in the sales tax to help fund public transportation. Four hundred adults are interviewed and 36% of them favor the proposal. Answer the next two questions.
1. The sample size for this sample survey appears to be
a) 400
b) 2,800,000
c) 144
d) 1,008,000
2. The 36% is a
a) Parameter
b) Margin of error
c) Chance of 144 people agreeing to the statement
d) Statistic
3. Event A occurs with probability 0.05. Event B occurs with probability 0.75. If A and B are disjoint, which statement is true?
a) P(A and B) = 0
b) P(A or B) = 0.80
c) P(A and B) = 0.0375
d) Both (a) and (b) are true.
4. Event A occurs with probability 0.05. Event B occurs with probability 0.75. If A and B are independent, which statement is true.
e) P(A and B) = 0
a) P(A or B) = 0.80
b) P(A and B) = 0.0375
c) Both (a) and (b) are true.
A marketing research firm wishes to determine if the adult men in Laramie, Wyoming would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to...

...the new point on the standarddeviation?
The new point has made the standarddeviation to go up to over 2.07
b) Follow the instructions to create the next two graphs then answer the following question: What did you do differently to create the data set with the larger standarddeviation.
What I did differently was to have two outliners on both ends of the outline so I can create the largerstandarddeviation and also to keep the mean at five.
2. Go back to the applet and put points matching each of the following data set into the first graph of the applet and clear the other two graphs. Set the lower limit to 0 and the upper limit to 100.
50, 50, 50, 50, 50
Notice that the standarddeviation is 0. Explain why the standarddeviation for this one is zero. Don’t show just the calculation. Explain in words why the standarddeviation is zero when all of the points are the same.
There’s not a deviation from this sample because all the data points are equal to each other.
3. Go back to the applet one last time and set all 3 of the lower limits to 0 and upper limits to 100. Then put each of the following three data sets into one of the graphs.
Data set 1: 0, 25, 50, 75, 100
Data set 2: 30, 40, 50, 60,...

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