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# Ch 6

### Normal probability distributions

3 properties for standard normal distribution 1)Its graph is bell shaped. 2) its mean is equal to o (u=0) 3)Its standard deviation is equal to 1
standard normal distribution is a normal probability distribution with mean=0 and standard deviation=1. the total area under the curve is = to 1
to find area,, probability, or percent of population use normal cdf: Normalcdf(left z score, right z score)
when shading forever to the left use ______ as your left number -9999
when shading forever to the right use ______ as your right number 9999
to find a z score corresponding to a known probability use _____ InvNorm(probabiliity that x < z)
critical values a z score on the borderline separating the z scores that are likely to occur from those that are unlikely. Notation: the expression Za denotes the z score with an area of a to its right.
Standardizing data value the z-score of a value is the number of standard deviations it is from the mean and can be obtained using the formula z=x-u/standard deviation
calculating probability that x lies between x1 and x2 in a normal distribution with mean and standard deviation use_______ nromalcdf(x1,x2, mean, standard deviation)
finding values from know probabilities use_____ InvNorm(probability that value < x, mean, standard deviation)
Central limit theorem tells us that for a population with any distributions, the distribution of the samle means approaches a normal distribution as the sample size increases
central limit theorem given_____ 1) the random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2) simple random samples all of size n are selected from the population.
Central limit theorem given___ continued... ^ continued... (The samples are selected so that all possible samples of teh same size n have the same chance of being selected
Central limit theorem- conclusions 1)the distibution of samle mean will, as the same size increases, apporach a normal distribution
Central limit theorem- conclusions continued... 2)the mean of the sample means is the population mean
Central limit theorem- conclusions continued... 3)the satndard deviation of all sample means is standard deviation/square root of n
Practical Rules commonly used 1)for sample of size n larger than 30, the distribution of the sample means can be approzimated reasonable well by a normal distribution. the approximation gets closer to a noraml distibution as sample size becomes larger.
Practical Rules commonly used continued 2)If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed (not just the values of n larger than 30)
Notations: mean of the sample means standard deviation of sample mean
When finding the probability of an outcome for an individual____ the standard deciation does not need to be adjusted.
When finding the probability for an outcome involving the mean of a randomly selected sample_____ the standard deciation of the sample means must be used. ( standard deviation/square root of n)
Created by: crickie11