Question

how much is in that can? the volume of beverage in a 12-ounces can is normally distributed with mean 12.06 ounces and standard deviation 0.04 ounces. (a) what is the probability that a randomly selected can will contain more than 12.08 ounces? (b) what is the probability that a randomly selected can will contain between 12 and 12.05 ounces? (c) is it unusual for a can to be under filled (contain less than 12 ounces)? round the answers to at least four decimal places. part: 0 / 30 of 3 parts complete part 1 of 3 the probability that a randomly selected can will contain more than 12.08 ounces is

Answer 1

This probability is greater than 0.05, a can filled less than 12 ounces is not unusual and P ( X > 12.08 )  = 0.3085.

X ~ N ( µ = 12.06 , σ = 0.04 )

P ( X > 12.08 )  = 1 - P ( X < 12.08 )

Standardizing the  value

Z = ( X - µ ) / σ

Z = ( 12.08 - 12.06 ) / 0.04

Z = 0.5

P (  ( X - µ ) / σ )  > ( 12.08 - 12.06 ) / 0.04 )

P ( Z > 0.5 )

P ( X > 12.08 )  = 1 - P ( Z < 0.5 )

P ( X > 12.08 )  =  1 - 0.6915

P ( X > 12.08 )  = 0.3085

b)

X ~  N ( µ = 12.06 , σ = 0.04 )

P ( 12 < X < 12.04 )

Standardizing the  value

Z = ( X - µ ) / σ

Z = ( 12 - 12.06 ) / 0.04

Z = -1.5

Z = ( 12.04 - 12.06 ) / 0.04

Z = -0.5

P ( -1.5 < Z < -0.5 )

P ( 12 < X < 12.04 )  =  P ( Z < -0.5 ) - P ( Z < -1.5 )

P ( 12 < X < 12.04 )  = 0.3085 - 0.0668

P ( 12 < X < 12.04 )  = 0.2417

c)

P ( X < 12 )

Standardizing the value

Z = ( X - µ  ) / σ

Z = ( 12 - 12.06 ) / 0.04

Z = -1.5

P (  ( X - µ ) / σ )  < ( 12 - 12.06 ) / 0.04 )

P ( X < 12 ) =  P ( Z < -1.5 )

P ( X < 12 ) = 0.0668

Since this probability is greater than 0.05, a can filled less than 12 ounces is not unusual .

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