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Answer:
865
Step-by-step explanation:
We have that in 95% confidence level the value of z has a value of 1.96. This can be confirmed in the attached image of the normal distribution.
Now we have the following formula:
n = [z / E] ^ 2 * (p * q)
where n is the sample size, which is what we want to calculate, "E" is the error that is 2% or 0.02. "p" is the probability they give us, 5 out of 50, is the same as 1 out of 10, that is 0.1. "q" is the complement of p, that is, 1 - 0.1 = 0.9, that is, the value of q is 0.9.
Replacing these values we are left with:
n = [1.96 / 0.02] ^ 2 * [(0.1) * (0.9)]
n = 864.36
865 by rounding to the largest number.
