Question

heights of tomato plants are Normally distributeda mean of 3.56 feet and a standard deviation of 0.25About% of tomato plants hathan or equal to 3.88 feet. Round thedecimal places, if necessary.but what percent of tomato plants have a height lessun or equal to 3.88 feet?e the z-table to answer the question.

Answer 1

We need to find the percentage of tomato plant that has a height less than or equal to 3.88 feet.

We know that the tomato plant heights are normally distributed with a mean of 3.56 ft and a standard deviation of 0.25 ft.

Thus, the percentage P(x≤3.88) of the heights being less than 3.88 can be calculated using the z-score z, given by:

$z=\frac{3.88-mean}{standard\text{ deviation}}$

Thus, we have:

$\begin{gathered} P(x\leq3.88)=P\left(z\leq\frac{3.88-3.56}{0.25}\right) \\ \\ P(x\leq3.88)=P\left(z\leq1.28\right) \end{gathered}$

Using a z-score table, we find that:

$P(z\leq1.28)\cong0.89973$

Therefore, the percent we are looking for is:

$P(x\leq3.88)\cong89.973\%\cong89.97\%$

Answer

About 89.97% of tomato plants.