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25 votes
25 votes
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.

User Roy Falk
by
2.9k points

1 Answer

6 votes
6 votes

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}}}=(38.5-250)/(9.4)=(-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.

User Daniele Tassone
by
2.8k points
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