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Chapter 6: Q 28. (page 358)

Give me some sugar! Machines that fill bags with powdered sugar are supposed to

dispense 32ounces of powdered sugar into each bag. Let x=the weight (in ounces) of the

powdered sugar dispensed into a randomly selected bag. Suppose that xcan be modeled

by a Normal distribution with mean 32ounces and standard deviation 0.6ounce. Find P(x≤31). Interpret this value.

Short Answer

Expert verified

About4.75%of all bags contain less than31ounces.

Step by step solution

01

Step 1. Given information. 

We have given values of meanμ=32, standard deviationσ=0.6andx=9.

02

Step 2. To find the probability. 

The z- score is the value decreased by the mean, divided by the standard deviation

z=x-μσ=31-320.6≈-1.67

Now,

P(x≤31)=P(Z<-1.67)=0.0475=4.75%

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