(a) Suppose we take a random sample of size 100 from a discrete distribution in this manner: A green die and a red die are thrown simultaneously 100 times and let Xi denote the sum of the spots on the two dice on the ith throw, i = 1, 2,...100. Find the probability that the sample mean number of spots on the two dice is less than 7.5.

(c) A circuit contains three resistors wired in series. Each is rated at 6 ohms. Suppose, however, that the true resistance of each one is a normally distributed random variable with a mean of 6 ohms and a standard deviation of 0.3 ohm. What is the probability that the combined resistance will exceed 19 ohms? How "precise" would the manufacturing process have to be to make the probability less than 0.005 that the combined resistance of the circuit would exceed 19 ohms?

n = 3
µ = 6µ[pic] = 6
σ = 0.3σ[pic] = 0.3 /[pic]

[pic]= 19 / 3

P ([pic]≥ 6.33)= 1- P ( Z < [pic] - µ[pic] )
σ[pic]
= 1 - P (Z < 6.33-6 )
0.3 /[pic]
= 1...

...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...

...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...

...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...

...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,...

...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...

...Kuleshov
Frequency Distributions
This assignment is based on Frequency Distributions and will include the following information:
1. The ability to describe the information provided by the StandardDeviation.
2. The ability to use the StandardDeviation to calculate the percentage of occurrence of a variable either above or below a particular value.
3. The ability to describe a normal distribution as...

...companies and the probability of getting a job offer there. These data are tabulated below. The tabulation is in the decreasing order of cost.
1. If the graduate applies to all 10 companies, what is the probability that she will get at least one offer?
2. If she can apply to only one company, base on cost and success probability criteria alone, should she apply to company 5? Why or why not?
3. If she applies to companies 2,5,8, and 9, what is...

...question: What is the impact of 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...

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