1) estimate the percent of boys wearing black bow ties by comparing the black section of the graph to the whole graph

2) calculate the percent of boys wearing each bow tie color. how does the percent wearing black bow ties compare to your estimate?

1. 30%

2. 33%

Step-by-step explanation:

1.

Judging by the size of the circle I would estimate it to be around 30% of the entire circle because it takes up a large portion of roughly half of the circle.

2.

To find the actual percentage of the black area, we first need to add all the values together.

Total Value = 22 + 18 + 13 + 8 + 66 + 48 + 25

Total Value = 200

Now we take the total value and divide it by the value of the black area alone and multiply it to 100.

Total Percentage = (66 / 200)

Total Percentage = 0.33 * 100

Total Percentage = 33%

a. The sample has more than 30 grade-point averages.

Step-by-step explanation:

Given that a researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of this sample

We are asked to find the conditions under which  that sample mean can be treated as a value from a population having a normal​ distribution

Recall central limit theorem here

The central limit theorem states that the mean of all sample means will follow a normal distribution irrespective of the original distribution to which the data belonged to provided that

i) the samples are drawn at random

ii) The sample size should be atleast 30

Hence here we find that the correct conditions is a.

Only option a is right

a. The sample has more than 30 grade-point averages.