Answer:
The probability that the sample proportion will be at least 3 percent more than the population proportion is 0.6157
Step-by-step explanation:
We need sample proportion between 0.75 - 0.03 = 0.72 and 0.75 +0.03 = 0.78. Here we have p = 0.75 and n= 158.
So z-score for sample proportion q = 0.72
z = =
= -
= - 0.872
So z-score for sample proportion q = 0.78
z= =
=
= 0.872
Therefore the probability that the sample proportion will be within 3 percent of the population proportion is
P( 0.72 < q < 0.78) = P ( -0.872 < z < 0.872)
= P( z < 0.872) - P( z < -0.872)
= 0.80785 - 0.19215
= 0.6157