Question

The number of Chocolate Chips in a bag is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

Determine the 29th percentile, (1197 Chips, I got that one)

Determine the number of Chocolate Chips in the bag that make up the middle 96% of bags.

What is the IQR of the number of Chocolate Chips in a bag of chocolate chip cookies?

Answer 1

The number of Chocolate Chips in a bag is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

Mean = 1262

SD = 118

Determine the 29th percentile.

X = Mean + Z*SD

Z for 29^th percentile = -0.55338

(by using z-table)

X = 1262 + (-0.55338)*118

X = 1262 - 0.55338*118

X = 1196.701

29^th percentile = 1197

Determine the number of Chocolate Chips in the bag that make up the middle 96% of bags.

Z critical values for middle 96% by using z-table are given as below:

Lower Z = -2.05375

Upper Z = 2.05375

Lower X = Mean + Z*SD = 1262 - 2.05375*118 =1019.658

Upper X = Mean + Z*SD = 1262 + 2.05375*118 = 1504.343

Answer: 1020 and 1504

What is the IQR of the number of Chocolate Chips in a bag of chocolate chip cookies?

IQR = Q3 – Q1

Z for Q3 = 0.67449

Z for Q1 = -0.67449

Q3 = Mean + Z*SD = 1262 + 0.67449*118 = 1341.59

Q1 = Mean + Z*SD = 1262 - 0.67449*118 = 1182.41

IQR = Q3 – Q1

IQR = 1341.59 - 1182.41

IQR = 159.18