2.a.) Assuming no change in the distribution the probability that the blackness of the spot is less than 1.0 is 48.01%. (1.0-1.005/.10= z-score of -.05 = .4801 or 48.01%)
b.) The probability that the blackness of the spot is between .95 and 1.0 is 18.89% (.95-1.005/.10=z score of -0.55 = 29.12%. take answer from #1 and subtract from this answer 48.01-29.12= 18.89%) c.) The probability that the blackness of the spot is between 1.0 and 1.05 is 19.35%. (1.05-1.005/.10= z-score of .45 = 67.36%, then take area from 1.0= 48.01% and subtract it from 67.36% and you get 19.35%) d.) The probability that the blackness of the spot would be less than .95 is 29.12%. The probability that the blackness of the spot would be greater than 1.05 is 32.64%. (Already solved for .95. Already solved for 1.05, therefore just took 1-the area for 1.05 and got 32.64%)

If the objective of the production team is to reduce the probability that the blackness is below 0.95 or above 1.05, I feel that the production team would be better off focusing on the process of improving the blackness to the target value of 1.0 rather than trying to reduce the standard further. The standard deviation is already relatively low at 0.10 which indicates little deviation from the mean value of 1.0 therefore reducing the standard deviation any further is just a waste.

3.e.) The probability that the average blackness of the 25 spots is less than 1.0 is 40.13%. (1.0-1.005/.10/square root of 25= standard error of .02= z-score of -0.25= 40.13%) f.) The probability that the average blackness of the 25 spots is between 0.95 and 1.0 is 39.83%. (Already solved for 1.0=40.13%, therefore .95-1.005/.02= z-score= -0.25= 0.3%. Then subtract the two= 39.83%) g.) The probability that the blackness of the spot is between 1.0 and 1.05 is 58.65%. (Already solved for 1.0=40.13%, therefore 1.05-1.005/.02= z-score= 2.25= 98.78%. Then 9878= 1.22%) i.) If the average blackness of today’s sample of 25...

...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 x....

...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...

...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...

...selected.
c) reasonably large due to the “cluster” effect.
d) 100 divided by the size of the population of Laramie.
Costs for standard veterinary services at a local animal hospital follow a Normal distribution with a mean of $80 and a standarddeviation of $20. Answer the next three questions.
8. Give the sample space for the costs of standard veterinary services.
a) {X ≥ 0}
b) { 0 ≤ X ≤ 80}
c) {0 ≤ X ≤ 160}...

...Standarddeviation can be difficult to interpret as a single number on its own. Basically, a small standarddeviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standarddeviation means that the values in the data set are farther away from the mean, on average.
The standarddeviation measures how concentrated the...

...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...

...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...

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