Crispy Chips is a potato chip company that is quite popular for its low-fat, low

Question

Crispy Chips is a potato chip company that is quite popular for its low-fat, low-calorie bags of potato chips. The procedure used at its production plant allows for 65 chips to be inserted into each bag for distribution to consumers. However, given that chip-making is not an exact science, there is a standard deviation of 4 chips per individual bag. If we can assume that the number of chips in each bag forms a normal distribution, calculate the following:

a) Calculate the z-score associated to 71 chips in a randomly-selected bag. [0.5]

b) Calculate the z-score associated to 60 chips in a randomly-selected bag. [0.5]

c) We know from the empirical rule that 95% of the scores should fall within 2 standard deviation units from the mean. What would be the minimum and maximum number of chips that would describe this range? [1 point]

Explanation / Answer

X: Number of chips inserted into the bag

X follows normal distribution with mean : 65 and standard devition '4'

(a) Z-score associated to 71 chips in a randomly selected bag

Z-Score for X = (X-Mean)/Standard deviation

Z-score for 71 = (71-65)/4 = 6/4 = 1.5

(b) the z-score associated to 60 chips in a randomly-selected bag

Z-score for 60 = (60-65)/4 = -5/4 = -1.25

(c) We know from the empirical rule that 95% of the scores should fall within 2 standard deviation units from the mean;

Minimum number of chips = Mean - 2 standard deviations = 65 - 2 x 4 = 65-8=57

Maximum number of chips = Mean + 2 standard deviations = 65 + 2 x 4 = 65 + 8 = 73

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