Question on Probability. What is my Z-Score 20?

Question

I have this homework but I am getting a z-score of 20? Why? Is my calculation wrong?

The question is

Without assuming that the diameters of apple pies are distributed according to the normal distributions, estimated the probability that the mean diameter is larger than 32 cm. The sample standard deviation is estimated to be 2. The sample mean is 28 and the sample size is 100.

When I used CLT (because the sample size is >30). I am getting a z score of 20? Is this correct?

Answer 1

Central Limit Theorem indicates that: For samples of size n taken from a population with mean, $\mu$, and a standard deviation, $\sigma$, $$\mu_{\overline{x}}=\mu, \sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}$$
This problem is actually a reversed form of CLT. We are told the sample mean and standard deviation, and we need to compute the population mean and standard deviation.
$$\sigma_{\overline{x}}=2=\frac{\sigma}{\sqrt{100}},\sigma=20$$$$\mu=\mu_{\overline{x}}=28$$
Thus it will just be $P(Z>\frac{32-28}{20})=P(Z>0.2)=1-P(Z<0.2)$

Answer 2

But isn't 2 the standard deviation and not the standard error? isn't the formula 32-28 divided by 2/SQ of 100? This would indeed have a Z value of 20.