# X: is the random variable that counts the number of successes in n trials. It has a binomial distribution. n: is the size of the sample. : is the proportion.

## Presentation on theme: "X: is the random variable that counts the number of successes in n trials. It has a binomial distribution. n: is the size of the sample. : is the proportion."— Presentation transcript:

X: is the random variable that counts the number of successes in n trials. It has a binomial distribution. n: is the size of the sample. : is the proportion of successes in the sample IT DOES NOT HAVE A BINOMIAL DISTRIBUTION!

So where did these formulas come from? Remember we started with : X was a random variable from a binomial distribution. 1) What are the 4 criteria for a binomial distribution? 2)What are the formulas for finding the mean and standard deviation for a binomial distribution.

Develop the formula for mean and standard deviation for asampling distribution Remember the population must be ten times as large as the sample size as a general rule of thumb of the standard deviation calculated this was is invalid.

The shape of the sampling distribution can be approximated with normal calculations as long as Do you recall why??????

p =.1, (1-p)=.9, n=15 p=.01 (1-p) =.99 n=15 np = 1.5 n(1-p) = 13.5 np =.15 n(1-p) = 14.85 p =.001, (1-p) =.999 n = 15 np =.015 n(1-p)= 14.985

p =.7 (1-p) =.3 np = 10.5 (1-p)n= 4.5 n=15 mean = 10.5 SD=1.7748239 p =.3 (1-p) =.7 np = mean= 4.5 n= 15 n(1-p) = 10.5 SD=1.7748 p =.9 (1-p) =.1 np = 13.5 (1-p)n= 1.5 n = 15, mean 13.5, SD = 1.161895

Example Your mal order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received that week for an audit. The audit reveals that 86 of these orders were shipped on time. What is the probability that the proportion in an SRS of 100 orders is as small as the proportion in your sample or smaller?

Checklist: 1) State the probability we are trying to find. 2) State the mean of this sample distribution. 3) State the standard deviation of the sampling distribution of Dont to forget to verify your assumption. 4) Can normal calculations be used?

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