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:
[tex]z=\frac{3.88-mean}{standard\text{ deviation}}[/tex]
Thus, we have:
[tex]\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}[/tex]
Using a z-score table, we find that:
[tex]P(z\leq1.28)\cong0.89973[/tex]
Therefore, the percent we are looking for is:
[tex]P(x\leq3.88)\cong89.973\%\cong89.97\%[/tex]
Answer
About 89.97% of tomato plants.