Problem

In a set of data, the value that is $-3$ standard…

03:15

Problem 26 Hard Difficulty

Two tomato plants were chosen from two groups of plants grown in different soils. Each sample plant produced 23 tomatoes The mean number of tomatoes for plants in the first soil was $17,$ with a standard deviation of $5 .$ The mean number of tomatoes for plants in the second soil was $18,$ with a standard deviation of $6 .$ Determine which plant, if either, is in the top 16$\%$ of its group.

Answer

Hence the plant which produces 23 tomatoes is in the top 16$\%$ of its group is the first plant
with mean 17 and standard deviation 5 .

Related Courses

Precalculus

Geometry

Intro Stats / AP Statistics

Algebra

Chapter 12

Probability And Statistics

Section 7

Normal Distributions

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Video Transcript

So here we have selected a plant from a two different samples of soil that produced 23 tomatoes. We want to decide whether it's in the top 16% of either soil sample, so we'll start with our 1st 1 Army nous 17 and our standard deviation is five. So we'll start by labeling. Our occurred we have 17 is are mean and then at the first Energy Aviation's we have 12 and 22 have the second standard deviations. We have seven and 27. So now, because it's normally distributed, we are can add the percentages that fall between standard deviations. So from our mean tow our first inter deviation as 34% of the data from the first inter deviation to the second is 13.5% and beyond. The second center deviation is to put by percent. So since we're looking for the top 16% that encompasses from the first inter deviation upward because 13.5 plus 2.5 is a 16%. So now we want to decide whether our sample plant falls within this area and it does because it is found here a 23. So we know that for our first sample that yes, our plant is in the top 16% for our second sample. We have a means of 18 and its energy ation of six. So we'll start by labeling our curve again. We have our remaining 18. Our first interview, aviation's. We have 12 and 24 at the second Seder Deviations. We have 30 and six and I have shaded in the top 16% again, which is again from the first standard deviation upward that our plant is located to the left of the first inter deviation. So it's not included in the area shaded, which means that no, it's not in the top 16%.

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