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Chapter 12: Problem 2

The height of six trees is measured. Is plant 6 taller than the median for all six trees? $$ \begin{array}{|c|c|} \hline \text { Plant } & \begin{array}{c} \text { Height } \\ \text { (inches) } \end{array} \\ \hline 1 & 67 \\ \hline 2 & 61 \\ \hline \end{array} $$ $$ \begin{array}{|c|c|} \hline 3 & 72 \\ \hline 4 & 71 \\ \hline 5 & 66 \\ \hline 6 & 68 \\ \hline \end{array} $$ (A) Yes, the median is 67.3 . (B) No, the median is 67.3 . (C) Yes, the median is 67.5 . (D) No, the median is 67.5 .

Short Answer

Expert verified
Yes, the median is 67.5.

Step by step solution

01

Arrange tree heights in order

First, we need to arrange the heights of the six trees in ascending order. The given heights are: 67, 61, 72, 71, 66, and 68. The sorted heights are: 61, 66, 67, 68, 71, and 72.
02

Calculate the median height

Since we have an even number of trees (6), the median will be the average of the middle two heights. The middle heights are 67 and 68. To find the average, add them together and divide by 2: \(\frac{67 + 68}{2} = 67.5\) So the median height is 67.5 inches.
03

Compare Plant 6's height to the median height

Now, we know Plant 6's height is 68 inches and the median height is 67.5 inches. Since 68 is greater than 67.5, Plant 6 is taller than the median height of all six trees. Based on our calculation, the correct answer is: (C) Yes, the median is 67.5.

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Most popular questions from this chapter

A mating is set up between two pure breeding strains of plants. One parent has long leaves and long shoots. The other parent has short leaves and stubby shoots. \(\mathrm{F}_{1}\) plants are collected, and all have long leaves and long shoots. \(\mathrm{F}_{1}\) plants are self-crossed, and \(1,000 \mathrm{~F}_{2}\) plants are phenotyped. The data is as follows: $$ \begin{aligned} &\text { Phenotype }\\\ &\\# \text { of } \end{aligned} $$ $$ \begin{array}{|l|r|} & \mathbf{F}_{2} \\ \hline \text { Long leaves, long shoots } & 382 \\ \hline \begin{array}{l} \text { Long leaves, stubby } \\ \text { shoots } \end{array} & 109 \\ \hline \text { Short leaves, long shoots } & 112 \\ \hline \begin{array}{l} \text { Short leaves, stubby } \\ \text { shoots } \end{array} & 397 \\ \hline \text { Total } & 1,000 \\ \hline \end{array} $$ Are the genes for leaf and shoot length segregating independently? (A) Yes; the degrees of freedom are \(3,\) and the calculated \(\chi^{2}\) value is small. (B) No; the degrees of freedom are 3, and the calculated \(\chi^{2}\) value is large. (C) Yes; the degree of freedom is \(1,\) and the calculated \(\chi^{2}\) value is small. (D) No; the degree of freedom is \(1,\) and the calculated \(\chi^{2}\) value is large.

In the following set of test scores, what is the mode and what is the range? Test Scores: \(71,67,75,65,66,32,69,70,72,82,\) 73,68,75,68,75,78 (A) Mode: 68; Range: 75 (B) Mode: 69; Range: 50 (C) Mode: 75; Range: 70.5 (D) Mode: 75; Range: 50

Five subjects were weighed before and after an 8 -week exercise program. What is the average amount of weight lost in pounds for all five subjects, rounded to the nearest pound? $$ \begin{array}{|c|c|c|} \hline \text { Subject } & \begin{array}{c} \text { Starting } \\ \text { Weight } \\ \text { (pounds) } \end{array} & \begin{array}{c} \text { Final } \\ \text { Weight } \\ \text { (pounds) } \end{array} \\ \hline 1 & 184 & 176 \\ \hline 2 & 200 & 190 \\ \hline 3 & 221 & 225 \\ \hline 4 & 235 & 208 \\ \hline 5 & 244 & 225 \\ \hline \end{array} $$ (A) 12 pounds (B) 13 pounds (C) 14 pounds (D) 15 pounds

Two pea plants are crossed, and a ratio of 3 yellow plants to 1 green plant is expected in the offspring. It is found that out of 100 plants phenotyped, 84 are yellow and 16 are green. Do the experimental data match the expected data? (A) Yes, the \(\chi^{2}\) value is greater than 3.84 . (B) Yes, the \(\chi^{2}\) value is smaller than 3.84 . (C) No, the \(\chi^{2}\) value is greater than \(3.84 .\) (D) No, the \(\chi^{2}\) value is smaller than \(3.84 .\)

Given the cross \(A a B b \times a a b b\), what is the probability of having an \(A a b b\) or aaBb offspring? (A) \(\frac{1}{2}\) (B) \(\frac{1}{4}\) (C) \(\frac{1}{16}\) (D) 0
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