# statistics

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25% of the houses in a certain area have swimming pools. if 5 houses from this area are selected at random, what is the probability that no one has a swimming pool.
1.1 at least two have swimming pools.

question2

an automatic boling machines fills cola into 2litre (200cm) bottles . aconsumer advoacate wants to test the null hypothesis that the average amount filled by the machine into a bottle is at least 2000cm. a random sample of 40 bottles coming out of the machine was selected and th e exact contents of the selected bottles was recorded. the sample mean was 1,9996cm. the population standard deviation is known from the past experience to be 1.30cm. test the null hypothesis at an @of 5%

For the first problem, you can use the binomial probability function, which states: P(x) = (nCx)(p^x)[q^(n-x)]
n = 5
x = 0 (for the first part)
p = .25
q = .75 (q = 1 - p)

For the first part: P(0) = (5C0)(.25^0)(.75^5)

I'll let you finish.

For the second part of that problem, find P(2) + P(3) + P(4) + P(5). Or you can take 1 - [P(0) + P(1)].

For the second question, you can probably use a one-sample z-test.
z = (sample mean - population mean) divided by (standard deviation divided by the square root of the sample size)

Compare the test statistic to the 5% level stated in the problem. Draw your conclusions from there.