Question

5. A local garden center says that a certain variety of tomato plant produces tomatoes with a mean weight of250 grams and a standard deviation of 42 grams. You take a random sample of 20 tomatoes produced by theseplants and calculate their mean weight x.

Answer 1

We know that, in this case, the sample mean will be equal to the population mean, so

$\mu_{\bar{x}}=250gr$

The standard deviation of the sample follows the following formula

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt[]{n}}=\frac{42gr}{\sqrt[]{20}}\approx9.4$

The sample standard deviation is 9.4, approximately.

At last, to find the probability of the sample, first, we have to find the z-score using the following equation

$z=\frac{x-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{38.5-250}{9.4}=\frac{-211.5}{9.4}=-22.5$

The probability value assigned to z = -22.5 is near to 0, which means that it is almost sure that there's no sample mean less than 38.5 grams.

Hence, the probability is around 0.0001.