Questions: The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. What is the percentile rank of a bag that contains 1450 chocolate chips? A bag that contains 1450 chocolate chips is in the th percentile. (Round to the nearest integer as needed.)

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips.
What is the percentile rank of a bag that contains 1450 chocolate chips?
A bag that contains 1450 chocolate chips is in the th percentile.
(Round to the nearest integer as needed.)

Transcript text: The number of chocolate chips in an 18 -ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. What is the percentile rank of a bag that contains 1450 chocolate chips? A bag that contains 1450 chocolate chips is in the $\square$ th percentile. (Round to the nearest integer as needed.)

Solution

Solution Steps

Step 1: Calculate the z-score

We are given a mean $\mu = 1252$ and a standard deviation $\sigma = 129$. We want to find the percentile rank for $x = 1450$ chocolate chips. We can calculate the z-score using the formula:

$z = \frac{x - \mu}{\sigma} = \frac{1450 - 1252}{129} = \frac{198}{129} \approx 1.53$

Step 2: Find the area to the left of the z-score

Using a z-table or calculator, we find the area to the left of $z = 1.53$ is approximately 0.9370. This represents the proportion of bags with fewer than 1450 chocolate chips.

Step 3: Calculate the percentile rank

The percentile rank is the percentage of data values that fall below a given value. In this case, we multiply the area to the left of the z-score by 100 to find the percentile rank.

Percentile rank $= 0.9370 \times 100 = 93.7$