Question

Software companies work hard to produce software without bugs. A particular company claims that 85% of the software it produces is bug free. A random sample of size 500 software programs was considered. (a) Calculate the mean of the sampling distribution of the sample proportion. (b) Calculate the standard deviation of the sampling distribution of the sample proportion. (Round your answer to four decimal places.)

Answer 1

Answer:

a) 0.85

b) 0.0160

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a saple of size n, the mean of the sampling distribution of sample means is p and the standard deviation is $s = \sqrt{\frac{p(1-p)}{n}}$

In this problem, we have that:

$p = 0.85, n = 500$

(a) Calculate the mean of the sampling distribution of the sample proportion.

By the Central Limit Theorem, 0.85

(b) Calculate the standard deviation of the sampling distribution of the sample proportion. (Round your answer to four decimal places.)

$s = \sqrt{\frac{0.85*0.15}{500}} = 0.0160$