Given a population with a proportion of 0.66. A random sample of 115 is obtained

Question

Given a population with a proportion of 0.66. A random sample of 115 is obtained. (a). What is the mean of the sampling distribution of the sample proportion? (b). What is the standard error of the sampling distribution of the sample proportion? Round your answer to 4 decimal places. Use the (c). Use the standard normal tables to find the fortieth percentile of the standard normal distribution closest z value (d), 60% of the time the sample proportion will be greater than what value? Round your answer to two decimal places. (Hint: use your answers from parts (a) to (c))

Explanation / Answer

p = 0.66 n = 115

(a) Mean = np = 115 * 0.66 = 75.9

(b) Standard deviation = (np(1-p)) = (75.9*0.34) = 5.0800

(c) 40th percentile corresponds to z value of -0.2534.

X = + z

= 75.9 - 0.2534 * 5.08

= 74.2167

(d) z value = 0.2534

X = + z

= 75.9 + 0.2534 * 5.08

= 77.1873.

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