A random sample of size n = 130 is taken from a population with population propo

Question

A random sample of size n = 130 is taken from a population with population proportion P = 0.58. Use Table 1. a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.) Expected value : Standard error : b. What is the probability that the sample proportion is between 0.50 and 0.70? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability : c. What is the probability that the sample proportion is less than 0.50? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability :

Explanation / Answer

n = 130
p = 0.58
SE = 0.58*0.42/sqrt(130) = 0.0214

expected value = mean = np = 130*0.58 = 75.4
std.dev. = sqrt(npq) = sqrt(130*0.58*0.42) = 5.6274

P(0.50 < p < 0.7)
= P((0.50 - 0.58)/0.0214 < z < (0.7 - 0.58)/0.0214))
= P(-3.7383 < z < 5.6075)
= 0.9999

P(p < 0.5)
= P(z<(0.50 - 0.58)/0.0214)
= P(z < -3.7383)
= 0.00009

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