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A normal distribution with a mean of 55 and a standard deviation of 6 is evaluated to solve a business problem. What is the probability that any value in the population is between 55 and 65?
Wiki User
∙ 14y ago
Convert to Std Normal Distribution and calculate (or use java script) area under curve for probability (see related links). Z55= (55-55)/6 = 0 and Z65 = (65-55)/6 = 1.667. We need area under curve for Z from 0 to 1.667. From javascript = use between 0 & 1.667, obtain .4522 or 45.22% probability. From Table; 0.9525-0.5 = .4525 = 45.25% (use above; more accurate but this IS close).
Wiki User
∙ 14y ago
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How is the expected value of a normal distribution computed?
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Let z1 be the smaller z value and z2 be the larger value. Let N(z) be the cumulative normal distribution evaluated at some value z. The random variable is Z. The probability that Z has a value from minus infinity to z2 is equal to N(z2). You can show this by drawing a bell shape curve, and shading in everything to the left of z2 as equal to the area under curve. Similarly, the probability that Z has a value from minus infinity to z1 is N(z1). The area under the bell curve (standard normal cumulative distribution) is N(z1) - N(z2). I can show this with a little example: z1= -1 z2 = 2 Area = N(2) - N(-1) = 0.9773 - 0.1587 = 0.8186. I used Excel with the normsdist(z) function. The mean is zero and standard deviation is one with this function.
Is it true that Risk should be evaluated solely by the magnitude or severity of expected harm?
false
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Step 3:Develop controls and make risk decisions. Develop control measures thateliminate the hazard or reduce its risk. As control measures are developed, risksare re-evaluated until the residual risk is at a level where the benefits outweighthe cost. The appropriate decision authority then makes the decision.
How do you find the probability between two values given the population mean and standard deviation?
The answer depends on the distribution of the random variable. For some variables it is easy to calculate the cumulative distribution, F(x).Then, the probability between the values p and q is F(q) - F(p). WARNING: This might need minor modification if the the distribution is discrete.The normal distribution is one which, in general, cannot be evaluated analytically. However, you can convert p and q to the x=corresponding z-score. If m is the mean and s the standard deviations, then z1 = (p - m)/s and z2 = (q - m)/s. The cumulative probability function for Z is tabulated (widely available online) and the probability between p and q is F(z2) - F(z1).Note, however, that sometimes the tabulated values are (Prob - 0.5), or are 1 - Prob(z) so read notes to the table.
How standard deviation formula can be used in in cement industry?
Usually, industrial use of standard deviation is involved in quality control and testing. A product such as cement, is produced in batches, and I assume, requires periodic testing to ensure consistent properties. The sample test variations can be evaluated using standard deviation. If the standard deviation is high, it is likely that inferior product could be shipped. Probability analysis can determine the chance that product below certain standards would be shipped.
How is the expected value of a normal distribution computed?
If a random variable X is distributed normally with probability distribution function p(x), then the expected value of X is E(X) = integral of x*p(x)dx evaluated over the whole of the real line.
What is gained by converting a raw score to a Z score?
The Gaussian (Normal) distribution is determined by two parameters: its mean and its variance. Each combination of these two parameters results in a different probability density function (pdf). Finding the probability based on raw scores would require values of the pdf relating to that particular combination of mean and variance. The pdf for the Gaussian distribution is not simple to calculate and it would be impossible to tabulate infinitely many of them. Instead, only the pdf for the Z-scores - the Standard Normal pdf - is tabulated. Any raw score is converted to a Z-score and the probability evaluated from the tables.
How do you find area under a curve between two z values?
Let z1 be the smaller z value and z2 be the larger value. Let N(z) be the cumulative normal distribution evaluated at some value z. The random variable is Z. The probability that Z has a value from minus infinity to z2 is equal to N(z2). You can show this by drawing a bell shape curve, and shading in everything to the left of z2 as equal to the area under curve. Similarly, the probability that Z has a value from minus infinity to z1 is N(z1). The area under the bell curve (standard normal cumulative distribution) is N(z1) - N(z2). I can show this with a little example: z1= -1 z2 = 2 Area = N(2) - N(-1) = 0.9773 - 0.1587 = 0.8186. I used Excel with the normsdist(z) function. The mean is zero and standard deviation is one with this function.
What does the higher standard deviation data set explain?
A higher standard deviation means that the data are fluctuating more widely with respect to the mean. It could mean there are some bad samples, or it could simply mean that the data are not as tightly bound to the mean as anticipated. An unexpected standard deviation should be evaluated, using more robust analyses techniques, so as to differentiate between the various explanations. This is an expected part of error analysis, without which an analysis is incomplete.
What should sources be evaluated for?
Sources should be evaluated for credibility, reliability, accuracy, and relevance to ensure the information is trustworthy and appropriate for the intended purpose. Check the author's credentials, publication date, potential biases, and supporting evidence to determine the credibility of a source.
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1-6 evaluated = -5
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Species are classified in nine groups, set through criteria such as rate of decline, population size, area of geographic distribution, and degree of population and distribution fragmentation.Extinct (EX) - No individuals remaining.Extinct in the Wild (EW) - Known only to survive in captivity, or as a naturalized population outside its historic range.Critically Endangered (CR) - Extremely high risk of extinction in the wild.Endangered (EN) - High risk of extinction in the wild.Vulnerable (VU) - High risk of endangerment in the wild.Near Threatened (NT) - Likely to become endangered in the near future.Least Concern (LC) - Lowest risk. Does not qualify for a more at risk category. Widespread and abundant taxa are included in this category.Data Deficient (DD) - Not enough data to make an assessment of its risk of extinction.Not Evaluated (NE) - Has not yet been evaluated against the criteria.When discussing the IUCN Red List, the official term "threatened" is a grouping of three categories: Critically Endangered, Endangered, and Vulnerable.
How are Market segments evaluated?
Market segments are evaluated as to their attractiveness or potential for generating revenue for the firm
Do architects get evaluated?
In the UK it is one of the longest and most difficult degrees to take, so yes they do get evaluated.
