Question

The amount X of beverage in a can labeled 12 ounces is normally distributed with mean...

The amount X of beverage in a can labeled 12 ounces is normally distributed with mean 12.1 ounces and standard deviation 0.05 ounce. A can is selected at random.

a. Find the probability that the can contains at least 12 ounces.

b. Find the probability that the can contains between 11.9 and 12.1 ounces.

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Answer #1

Given: = 12.1, = 0.05

To find the probability, we need to find the Z scores first.

Z = (X - )/

(a) P(X 12) = 1 - P(X < 12)

P(X < 12), Z = (12 - 12.1)/0.05 = -2

The probability is = 0.0228

The required probability for P(X > 21) =1 - 0.0228 = 0.9772

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(13) P(11.9 < X < 12.1) = P(X < 12.1) - P(X < 11.9)

For P(X < 12.1); Z = (12.1 – 12.1)/0.05 = 0

The probability for P(X < 12.1) = 0.5

For P(X < 11.9); Z = (11.9 – 12.1)/0.05 = -4

The probability for P(X < 11.9) = 0.00

Therefore the required probability = 0.5000 - 0.000 = 0.5000

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