10 Points (1) ASPE 6ed Problem 4-76, page 127 4-76. + The fill volume of an auto

Question

10 Points (1) ASPE 6ed Problem 4-76, page 127 4-76. + The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce. (a) What is the probability that a fill volume is less than 12 fluid ounces? (b) If all cans less than 12.1 or more than 12.6 ounces are scrapped, what proportion of cans is scrapped? (e) Determine specifications that are symmetric about the mean that include 99% of all cans. (2) ASPE 6ed Problem 4-104, page 132 parts b and c only

Explanation / Answer

Mean = 12.4 fluid ounces

Standard deviation = 0.1 fluid ounces

P(X < A) = P(Z < (A - mean) / standard deviation)

a) P(X < 12) = P(Z < (12 - 12.4)/0.1)

= P(Z < -4)

= 0

b) P(scrapped) = P(X<12.1) + P(X > 12.6)

= P(X < 12.1) + 1 - P(X < 12.6)

= P(Z < (12.1 - 12.4)/0.1) + 1 - P(Z < (12.6 - 12.4)/0.1)

= P(Z < - 3) + 1 - P(Z < 2)

= 0.0013 + 1 - 0.9772

= 0.0241

c) Let the upper and lower limits be M and N

P(X < M) = (1-0.99)/2 = 0.005

P(X < (M - 12.4)/0.1) = 0.005

(M - 12.4)/0.1 = -2.56

M = 12.4 - 0.256

= 12.144 fluid ounces

N = 12.4 - 0.256

= 12.656 fluid ounces

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