Suppose a simple random sample of size n 1000 is obtained f

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.76. Complete parts (a) through (c) below. Describe the sampling distribution of p. What is the probability of obtaining x = 790 or more individuals with the characteristic? What is the probability of obtaining x = 740 or fewer individuals with the characteristic?

Solution

As you have already computed P(x>=790), there is a shortcut to calculating P(x<=740)

P(x<=740)

=P(x>740)

However, in case of normal approximation, which is valid in this case, P(X>740) = P(X>=740)

Therefore, use the same formula as the last part, and switch 790 with 740.