Question

One of the authors with too much time on his hands weighed each chocolate candy in a bag of 463 plain chocolate candies. Complete parts​ (a) through​ (c).a. One of the chocolate candies weighed 0.776 gram and it was heavier than 25 of the other chocolate candies. What is the percentile of this particular​ value?It is the __th percentile. ​(Round down to the nearest integer as​ needed.)b. One of the chocolate candies weighed 0.876 gram and it was heavier than 329 of the other chocolate candies. What is the percentile of this particular​ value?It is the ___th percentile. ​(Round down to the nearest integer as​ needed.)c. One of the chocolate candies weighed 0.856 gram and it was heavier than 229 of the other chocolate candies. What is the percentile of this particular​ value?It is the ___th percentile. ​(Round down to the nearest integer as​ needed.)

Answer 1

Answer:

a. One of the chocolate candies weighed 0.776 gram and it was heavier than 25 of the other chocolate candies. What is the percentile of this particular​ value?

It is the 5th percentile.

b. One of the chocolate candies weighed 0.876 gram and it was heavier than 329 of the other chocolate candies. What is the percentile of this particular​ value?

It is the 71th percentile.

c. One of the chocolate candies weighed 0.856 gram and it was heavier than 229 of the other chocolate candies. What is the percentile of this particular​ value?

It is the 49th percentile.

Step-by-step explanation:

So when we are talking about percentile, what it means is the point below a certain score or percentage lies, or the rank.

The formula is simple:

Let's call percentile pth, pth=$\frac{p}{100}*(n+1)$

where p is the position in the data set you want to evaluate (in statistical analysis, these are called quartiles, and they are useful for evaluating groups, so 3 quartiles would divide sample into 25th, 50th and 75th, four quartiles would be 20th, 40th, 60th, 80th, and so on).

and n is the number of elements in the set

For this problem there are no quartiles specified, but we can then work with the definition of percentile, meaning, if you are the 5th percentile, then 95% of the group are above you.

a. So 0.776 was heavier than 25 others, meaning it is in the 26th position out of 463. But we need that in relation to 100, so $\frac{26}{463}$ is 0.0562 or about 5/100, (rounded down). That would mean that the percentile is:

pth=$\frac{26}{463}$*100=5.62 or 5, rounded down

b. 0.876 was heavier than 329 others, meaning it is in the 330th position out of 463. In relation to 100, so $\frac{330}{463}$ is 0.7127 or about 71/100, (rounded down). That would mean that the percentile is:

pth=$\frac{330}{463}$*100=71.27 or 71, rounded down

c. 0.856 was heavier than 229 others, meaning it is in the 230th position out of 463. In relation to 100, so $\frac{230}{463}$ is 0.4967 or about 49/100, (rounded down). That would mean that the percentile is:

pth=$\frac{230}{463}$*100=49.67 or 49, rounded down