Question

At the Fisher farm, the weights of zucchini squash are Normally distributed. Which standardized weight represents the top 10% of the zucchinis?

Find the z-table here.

–1.64
–1.28
1.28
1.64

Answer 1

Thus, the standardized weight which represents the top 10% of the zucchinis from the z-table for the fisher farm is 1.28.

How to get the z scores?

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

$Z = \dfrac{X - \mu}{\sigma}$

Here, X is sample, is μ mean and is σ standard deviation.

At the Fisher farm, the weights of zucchini squash are Normally distributed.

For the normal distribution let the value of mean is 0 and standard deviation 1. Thus,

$Z = \dfrac{X - \mu}{\sigma}\\Z = \dfrac{X - 0}{1}\\Z=X$

For the top 10% of the zucchinis, the value of α is 0.9. From the table for this value the z score is,

$Z=X=1.28$

Thus, the standardized weight which represents the top 10% of the zucchinis from the z-table for the fisher farm is 1.28.

Learn more about the z score here;

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