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Using the standard normal distribution find the probability that z is greater than 1.78?
0.0375
What are the advantages of using standard normal distribution over the normal distribution?
The standard normal distribution is tabulated. The critical values for various outcomes can therefore be worked out easily from tables. The normal distribution is extremely difficult to integrate: most people, even with a university degree in mathematics will be unable to do so. So working out the probability of events from the normal distribution is near enough impossible.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
How do you solve a standard normal distribution?
You do not solve a standard normal distribution. It is not a question nor an equation or inequality to be solved. You can answer questions using the standard normal distribution but what you do depends on the question and on what information is given.
What are the advantages of using the standard normal distribution over the normal distribution?
There is no simple formula to calculate probabilities for the normal distribution. Those for the standard normal have been calculated by numerical methods and then tabulated. As a result, probabilities for the standard normal can be looked up easily.
Using the standard normal distribution find the probability that z is greater than 1.78?
0.0375
What are the advantages of using standard normal distribution over the normal distribution?
The standard normal distribution is tabulated. The critical values for various outcomes can therefore be worked out easily from tables. The normal distribution is extremely difficult to integrate: most people, even with a university degree in mathematics will be unable to do so. So working out the probability of events from the normal distribution is near enough impossible.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
How do you solve a standard normal distribution?
You do not solve a standard normal distribution. It is not a question nor an equation or inequality to be solved. You can answer questions using the standard normal distribution but what you do depends on the question and on what information is given.
What are the advantages of using the standard normal distribution over the normal distribution?
There is no simple formula to calculate probabilities for the normal distribution. Those for the standard normal have been calculated by numerical methods and then tabulated. As a result, probabilities for the standard normal can be looked up easily.
How do you find the z multiplier?
In the field of analytical measurement, the z-multiplier is a measure of error. It indicates a statistical probability of error. It is calculated using standard formulas for normal distribution.
How the normal distribution could be transformed to a standard normal distribution?
You may transform a normal distribution curve, with, f(x), distributed normally, with mean mu, and standard deviation s, into a standard normal distribution f(z), with mu=0 and s=1, using this transform: z = (x- mu)/s
What can be determined using theoretical probability?
The probability distribution function.
What is the probability of P z-0.41 using the standard normal distribution?
See the related link for the area at 0.41 (same as -0.41) which is 0.1591. This area, which is the probability, is from minus infinity to -0.41. If you want the area from -0.41 to plus infinity you need to take 1 - 0.1591 which is 0.8409.
The average time for project completion using PERT method is 32 weeks, with a standard deviation of the longest path being 4 weeks. using the Y value table for normal distribution curve, find the:(a) probability of completing the project in 32 weeks?
Th
Can the Empirical Rule of probability be applied to the uniform probability distribution?
Yes, except that if you know that the distribution is uniform there is little point in using the empirical rule.
What is Hypothesis Testing of Goodness-of-Fit?
A test using relative errors comparing a frequency table to the expected counts determined using a given probability distribution; the null hypothesis is that the given probability distribution fits the data's distribution.
