The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. (a) what is the probability that a randomly selected bag contains between 10001000 and 15001500 chocolate chips? (b) what is the probability that a randomly selected bag contains fewer than 10251025 chocolate chips? (c) what proportion of bags contains more than 11751175 chocolate chips? (d) what is the percentile rank of a bag that contains 10501050 chocolate chips?

A) 0.947; B) 0.0392; C) 0.7257; D) 6th

Step-by-step explanation:

For part A,

We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.

Using a z-table, we see that the area to the right of z = -1.95 is 0.0256.  The area to the right of z = 1.92 is 0.9726.  This means the area between them is

0.9726 - 0.0256 = 0.947.

For part B,

To find the probability that fewer than 1025 chips are in the bag, we find the z-score:

Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.

For part C,

Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this.  To find the proportion greater than this, we subtract from 1:

In the z-table, we see that the area under the curve less than this is 0.2743.  This means that the area greater than this is 1-0.2743 = 0.7257.

For part D,

We again find the area under the curve less than this.  This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.

In the z-table, we see the area to the right of this is 0.0582.  This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.