Question

A company produces packets of soap powder labeled "Giant Size 20 oz." The actual weight of soap powder in such a box has a Normal distribution with a mean of 21 oz and a standard deviation of 0.5 oz. To avoid dissatisfied customers, a box of soap is considered underweight if it weighs less than 20 oz. To avoid losing money, the top 5% (the heaviest 5%) is labeled overweight.

How heavy does a box have to be in order for the box to be labeled overweight?

oz Round to 2 places.

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Answer 1

X ~ N ( µ = 21 , σ = 0.5 )
P ( X > x ) = 1 - P ( X < x ) = 1 - 0.05 = 0.95
To find the value of x
Looking for the probability 0.95 in standard normal table to calculate Z score = 1.6449
Z = ( X - µ ) / σ
1.6449 = ( X - 21 ) / 0.5
X = 21.82