The number of chocolate chips in a bag of chocolate is approximately normally di

Question

The number of chocolate chips in a bag of chocolate is approximately normally distributed with a mean of 1261 chips and a standard deviation of 117 chips. (a) Determine the 26th 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 97% of bags. (a) The 26th percentile for the number of chocolate chips in a bag of chocolate chip cookies is chocolate chips. (Round to the nearest which number as needed.) (b) The number of chocolate chips in a bag that make up the middle 97% of bag is to chocolate chips (Round to the nearest whole number as needed Use order.)

Explanation / Answer

a)

From the normal distribution table, the 26th percentile is -0.64:
P( z < -0.64 ) = 0.26

z = (x - ) /
-0.64 = ( x-1261) / 117
x-1261 = (117)(-0.64)
x = 1261 + (-0.64)(117)
x = 1186.12

b)
From the normal distribution table, P( -2.176 < z < 2.176) = 0.97
z = (x - ) /
-2.176 = (x - 1261) /117
x = 1261 - (2.176)(117)
x = 1006.408

2.176 = (x - 1261) /117
x = 1261 + (2.176)(117)
x = 1515.592

1515.592 - 1006.408 = 509.184
510 chocolate chips in the bag make up the middle 97% .

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