The number of chocolate chips in a bag of chocolate chip cookies is approximatel

ID: 3065249 • Letter: T

Question

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of

1263

chips and a standard deviation of

117

chips. (a) Determine the

30th

percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle

96%

of bags.

(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?

(a) The

30th

percentile for the number of chocolate chips in a bag of chocolate chip cookies is

1202

chocolate chips.

(Round to the nearest whole number as needed.)

(b) The number of chocolate chips in a bag that make up the middle

96%

of bags is

nothing

chocolate chips.

(Round to the nearest whole number as needed. Use ascending order.)

From the normal distribution table, the 29th percentile is -0.55:
P( z < -0.5244) = 0.29

z = (x - ) /
-0.5244 = ( x-1263) / 117
x-1263 = (117)(-0.5244)
x = 1201.6452

b)
From the normal distribution table, P( -2.054 < z < 2.054) = 0.96
z = (x - ) /
-2.054 = (x - 1263) /117
x = 1263 - (2.054)(117)
x = 1022.682

2.054 = (x - 1261) /118
x = 1261 + (2.054)(118)
x = 1503.318

hence there are 1023 to 1503 chips in the middle 96% of bags

IQR = Q3 - Q1

Q3 = 1263 + 0.6745*117 = 1341.9165

Q1 = 1263 - 0.6745*117 = 1184.084

IQR = 157.33

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