The probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5 is approximately 0.106, rounded off to the third decimal place.
The mean of the distribution of the hourly rate of registered web developers is $\mu = 35$ and the standard deviation is $\sigma = 4$. We are interested in finding the probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5$.
We can use the central limit theorem to approximate the sampling distribution of the sample mean. According to the central limit theorem, the sampling distribution of the sample mean will be approximately normal with mean $\mu_{\bar{x}} = \mu = 35$ and standard deviation $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{4}{{100}} = 0.4$.
Let $X$ be the sample mean hourly rate of the 100 registered web developers. Then we need to find $P(X > 35.5)$.
Standardizing $X$,we get:
Using a standard normal table or calculator, we can find the probability $P(Z > 1.25) \approximately 0.1056$. Therefore, the probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5$ is approximately 0.106, rounded off to the third decimal place