find the values of the 30th and 90th percentiles of the data.
129, 113, 200, 100, 105, 132, 100, 176, 146, 152
a. 30th percentile = 105;
90th percentile = 200
b. 30th percentile = 113;
90th percentile = 200
c. 30th = 105;
90th = 176
d. 30th = 113;
90th = 176

30th percentile = 109

Solution:

Step 1. Arrange the data in ascending order: 100, 100, 105, 113, 129, 132, 146, 152, 176, 200

Step 2. Compute the position of the pth percentile (index i):

i = (p / 100) * n), where p = 30 and n = 10

i = (30 / 100) * 10 = 3

Step 3. The index i is an integer ⇒ the 30th percentile is the average of the values in the 2th and 3th positions (105 and 113 respectively)

the 30th percentile is (105 + 113) / 2 = 109

90th percentile = 188

Solution:

Step 1. Arrange the data in ascending order: 100, 100, 105, 113, 129, 132, 146, 152, 176, 200

Step 2. Compute the position of the pth percentile (index i):

i = (p / 100) * n), where p = 90 and n = 10

i = (90 / 100) * 10 = 9

Step 3. The index i is an integer ⇒ the 90th percentile is the average of the values in the 8th and 9th positions (176 and 200 respectively)

the 90th percentile is (176 + 200) / 2 = 188

You might have to round them according to the problem's instructions.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40