Suppose that 60 percent of the employees in a particular union support a candidate for union president.The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 4 percentage points of the actual proportion is _____.
A)0.9786
B)0.9878
C)0.9902
D)0.5398
E)0.8413

Question

Quizplus · Accepted Answer

To find the probability, we need to use the normal approximation to the binomial distribution.

Using the sample proportion formula, we have:

p-hat = 0.6 
n = 1000

The standard deviation of the sample proportion is:

sqrt((0.6 * 0.4) / 1000) = 0.015

We want to find the probability that the sample proportion falls within 4 percentage points of the actual proportion. This means that we want to find the probability that:

0.56 ≤ p-hat ≤ 0.64

We can convert these values into z-scores:

z1 = (0.56 - 0.6) / 0.015 = -2.67 
z2 = (0.64 - 0.6) / 0.015 = 2.67

Using a standard normal distribution table or a calculator, we can find that the probability of z being between -2.67 and 2.67 is approximately 0.9902. Therefore, the probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 4 percentage points of the actual proportion is 0.9902.

Suppose That 60 Percent of the Employees in a Particular