Question

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.

**?(a)** What is the probability that a randomly
selected bag contains between 1100 and 1400 chocolate? chips?

**?(b)** What is the probability that a randomly
selected bag contains fewer than 1025 chocolate? chips?

**?(c)** What proportion of bags contains more than
1200 chocolate? chips?

**?(d)** What is the percentile rank of a bag that
contains 1050 chocolate? chips?

Answer #1

= 1252

= 129

(a)

To find P(1100 < X < 1400):

Case 1: For X from 1100 to mid value:

Z = (1100 - 1252)/129 = - 1.1783

Table of Area Under Standard Normal Curve gives area = 0.3810

Case 2: For X from mid value to 1400:

Z = (1400 - 1252)/129 = 1.1473

Table gives area = 0.3749.

So,

P(1100 < X < 1400) = 0.3810 + 0.3749 = 0.7559

(b) To find P(X<1025):

Z = (1025 - 1252)/129 = - 1.7597

Table gives area = 0.4608

So,

P(X<1025) = 0.5 - 0.4608 = 0.0392

(c) Ro find P(X>1200):

Z = (1200 - 1252)/129 = - 0.4031

Table gives area = 0.1554

So,

P(X>1200) = 0.5 + 0.1554 = 0.6554

(d)

Z = (1050 - 1252)/129 = - 1.5659

Table gives area = 0.4418

So,

Percentile rank = (0.5 - 0.4418)X100 = 5.82 %

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