HW - 7.2
Part 3 of 4
Points: 0.25 of 1
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standar
(a) What is the probability that a randomly selected bag contains between 1000 and 1500 chocolate chips?
(b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips?
(c) What proportion of bags contains more than 1200 chocolate chips?
(d) What is the percentile rank of a bag that contains 1000 chocolate chips?
Click the icon to view a table of areas under the normal curve.
(a) The probability that a randomly selected bag contains between 1000 and 1500 chocolate chips is 0.9473
(Round to four decimal places as needed)
(b) The probability that a randomly selected bag contains fewer than 1125 chocolate chips is 0.1624
(Round to four decimal places as needed.)
(c) The proportion of bags that contains more than 1200 chocolate chips is $\square$
(Round to four decimal places as needed.)
liew an example
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Step 1 ：The problem is asking for the proportion of bags that contains more than 1200 chocolate chips. This is a problem of finding the probability of a value in a normal distribution.

Step 2 ：The formula for finding the z-score of a value in a normal distribution is \( (X - \mu) / \sigma \), where X is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 3 ：Once we have the z-score, we can find the probability associated with it using a z-table or a function that gives the cumulative distribution function of the normal distribution.

Step 4 ：However, since we want the proportion of bags that contains more than 1200 chocolate chips, we need to subtract the cumulative probability from 1.

Step 5 ：Given that the mean is 1252, the standard deviation is 18, and the value is 1200, we can calculate the z-score as \( -2.888888888888889 \).

Step 6 ：Using this z-score, we can find the cumulative probability as \( 0.9980669717300181 \).

Step 7 ：Finally, subtracting this cumulative probability from 1 gives us the proportion of bags that contains more than 1200 chocolate chips.

Step 8 ：The final answer is \(\boxed{0.9981}\).