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Variance and the Standard Deviation

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In San Francisco, 30% of workers take public transportation daily.
a) In a sample of 10 workers, what is the probability that exactly three workers take the public transport daily? [Hint: It is a Binomial Distribution Problem.]

f(3) =

b) In a sample of 10 workers, what is the probability that at least three workers take the public transport daily?

P(x?3)=1-f(0)- f(1)- f(2)
f(0) =
f(1) =
f(2) =
P(x?3)=1-f(0)- f(1)- f(2) =

c) How many workers are expected to take the public transportation daily?

E(X) =

d) Compute the variance and the standard deviation of the number of workers that will take the public transport daily.

Var(X) =
Standard Deviation =

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What would be the mean, variance, standard deviation and shape of the distribution of sample means?

If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers.

Note: Variance is the square of the standard deviation.

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