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A population proportion is 0.59 . Suppose a random sample of 660 items is sampled randomly from this population.
Appendix ASt
a. What is the probability that the sample proportion is greater than 0.62 ?
b. What is the probability that the sample proportion is between 0.54 and 0.63 ?
c. What is the probability that the sample proportion is greater than 0.57 ?
d. What is the probability that the sample proportion is between 0.54 and 0.55 ?
e. What is the probability that the sample proportion is less than 0.49 ?
(Round values of $z$ to 2 decimal places, e.g. 15.25 and final answers to 4 decimal places, eg. 0.2513.)
a.
b.

Step 1 ：Given that the population proportion is 0.59 and a random sample of 660 items is taken from this population.

Step 2 ：We are asked to find the probability that the sample proportion is greater than 0.62.

Step 3 ：This is a problem of normal approximation to the binomial distribution. The sample proportion follows a normal distribution with mean equal to the population proportion (0.59) and standard deviation equal to the square root of \((0.59)(1-0.59)/660\).

Step 4 ：We need to calculate the z-score for 0.62, which is \((0.62-0.59)\) divided by the standard deviation.

Step 5 ：Then we can use the standard normal distribution to find the probability that the z-score is greater than the calculated value.

Step 6 ：The calculated z-score is approximately 1.57.

Step 7 ：The probability that the sample proportion is greater than 0.62 is approximately 0.0586.

Step 8 ：Final Answer: The probability that the sample proportion is greater than 0.62 is \(\boxed{0.0586}\).