Question

Assuming that p equals .60 and the sample size is 1,000, what is the probability of observing a sample proportion that is at least .64?

Answer 1

Answer:

Therefore the probability of observing a sample proportion that is at least 0.64 =  P(Z ≥ 2.58)  =  1 - P(Z < 2.58) = 1 - 0.9951 = 0.0049

Step-by-step explanation:

It is given that p = 0.6

This is also the mean of the sample

Therefore q  =  1 - p  = 1 - 0.6  = 0.4

The sample size, n = 1000

Therefore standard deviation of the sample  = $\sqrt{\frac{p\times q}{n} } = \sqrt{\frac{0.6\times 0.4}{1000} } = \sqrt{\frac{0.24}{1000} } = 0.0155$

Z value for the sample proportion that is at least 0.64 $= \frac{0.64 - 0.6}{0.0155} = 2.58$

Therefore the probability of observing a sample proportion that is at least 0.64 =  P(Z ≥ 2.58)  =  1 - P(Z < 2.58) = 1 - 0.9951 = 0.0049