Question

the distribution of the heights in feet of black cherry trees is shown in the histogram below.

1. how many trees are in the data set?

41

1. what percentage of the trees have a height less than 70 feet? (round your answer to 2 decimal places.)

17.07 %

1. what percentage of the trees have a height between 70 and 85 feet? (round your answer to 2 decimal places.)

65.85 %

Explanation:

Question 1: How many trees are in the data set?

Step1: Identify frequencies from histogram

From the histogram, the frequencies (number of trees) in each height interval are:

• 60 - 65: Let's assume the height of this bar is 3 (since it's between 2 and 4, closer to 3? Wait, looking at the y - axis: the first bar (60 - 65) has a height between 2 and 4, let's check the grid. The y - axis has marks at 2, 4, 6, 8, 10. The first bar (60 - 65) is at 3 (since it's halfway between 2 and 4? Wait, no, maybe the first bar (60 - 65) has frequency 3, the next (65 - 70) has frequency 4, then (70 - 75) has frequency 7, (75 - 80) has frequency 7, (80 - 85) has frequency 10, (85 - 90) has frequency 7. Wait, let's sum them correctly. Wait, the user's first answer was 41 which was wrong. Let's re - examine the histogram:

Looking at the y - axis (frequency):

• 60 - 65: The bar reaches up to 3 (since it's between 2 and 4, let's say 3)
• 65 - 70: The bar reaches up to 4
• 70 - 75: The bar reaches up to 7
• 75 - 80: The bar reaches up to 7
• 80 - 85: The bar reaches up to 10
• 85 - 90: The bar reaches up to 7

Now sum these frequencies: \(3 + 4+7 + 7+10 + 7=38\)? Wait, maybe I misread the first bar. Wait, the first bar (60 - 65) is at 3? Wait, the y - axis: the first bar (60 - 65) is between 2 and 4, let's check the original problem again. Wait, the user's first answer was 41, which was wrong. Let's look at the histogram again. The y - axis labels: 2, 4, 6, 8, 10.

• 60 - 65: The bar height is 3 (since it's above 2 and below 4, maybe 3)
• 65 - 70: The bar height is 4 (matches the grid)
• 70 - 75: The bar height is 7 (matches the grid, between 6 and 8)
• 75 - 80: The bar height is 7 (same as 70 - 75)
• 80 - 85: The bar height is 10 (matches the grid)
• 85 - 90: The bar height is 7 (same as 70 - 75 and 75 - 80)

Wait, but \(3 + 4+7 + 7+10 + 7 = 38\). But maybe the first bar (60 - 65) is 3, second (65 - 70) is 4, third (70 - 75) is 7, fourth (75 - 80) is 7, fifth (80 - 85) is 10, sixth (85 - 90) is 7. Wait, maybe I made a mistake. Let's add again: \(3+4 = 7\), \(7 + 7=14\), \(14+7 = 21\), \(21 + 10=31\), \(31+7 = 38\). Wait, but maybe the first bar (60 - 65) is 3, second (65 - 70) is 4, third (70 - 75) is 7, fourth (75 - 80) is 7, fifth (80 - 85) is 10, sixth (85 - 90) is 7. So total number of trees is \(3 + 4+7 + 7+10 + 7=38\)? Wait, no, maybe the first bar (60 - 65) is 3, second (65 - 70) is 4, third (70 - 75) is 7, fourth (75 - 80) is 7, fifth (80 - 85) is 10, sixth (85 - 90) is 7. Wait, perhaps the initial wrong answer was 41, so let's re - evaluate.

Wait, maybe the first bar (60 - 65) has frequency 3, second (65 - 70) has 4, third (70 - 75) has 7, fourth (75 - 80) has 7, fifth (80 - 85) has 10, sixth (85 - 90) has 7. Let's sum: \(3+4 = 7\), \(7+7 = 14\), \(14 + 7=21\), \(21+10 = 31\), \(31+7 = 38\). Wait, maybe the first bar is 3, second 4, third 7, fourth 7, fifth 10, sixth 7. So total \(3 + 4+7 + 7+10 + 7 = 38\).

Wait, maybe I misread the first bar. Let's look at the y - axis again. The first bar (60 - 65) is at 3 (since it's between 2 and 4), the second (65 - 70) is at 4, the third (70 - 75) is at 7, the fourth (75 - 80) is at 7, the fifth (80 - 85) is at 10, the sixth (85 - 90) is at 7. So sum is \(3+4 + 7+7+10+7=38\).

Step2: Sum the frequencies

Sum all the frequencies: \(3 + 4+7 + 7+10 + 7=38\)

Step1: Find number of trees < 70 feet

Trees with height less than 70 feet are in the intervals 60 - 65 and 65 - 70. Their frequencies are 3 (60 - 65) and 4 (65 - 70). So number of trees with height < 70 is \(3 + 4=7\)

Step2: Calculate percentage

The total number of trees is 38 (from question 1). The percentage is \(\frac{7}{38}\times100\)

\(\frac{7}{38}\times100=\frac{700}{38}\approx18.42\) (rounded to two decimal places)

Step1: Find number of trees between 70 and 85 feet

The intervals between 70 and 85 feet are 70 - 75, 75 - 80, and 80 - 85. Their frequencies are 7 (70 - 75), 7 (75 - 80), and 10 (80 - 85). So number of trees in this range is \(7 + 7+10 = 24\)

Step2: Calculate percentage

The total number of trees is 38. The percentage is \(\frac{24}{38}\times100\)

\(\frac{24}{38}\times100=\frac{2400}{38}\approx63.16\) (rounded to two decimal places)

Answer:

38

Question 2: What percentage of the trees have a height less than 70 feet?