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 = [tex]\sqrt{\frac{p\times q}{n} } = \sqrt{\frac{0.6\times 0.4}{1000} } = \sqrt{\frac{0.24}{1000} } = 0.0155[/tex]
Z value for the sample proportion that is at least 0.64 [tex]= \frac{0.64 - 0.6}{0.0155} = 2.58[/tex]
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
