Question

A bottling company uses a filling machine to fill plastic bottles with a popular cola. The...

A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean µ=303 ml and standard deviation σ= 5 ml

    1. What is the probability that an individual bottle contains greater than 305 ml?
    2. What is the probability that the sample mean of 100 bottles is less than 302 ml?
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Answer #1

a)

Given,

= 303 , = 5

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

So,

P(X > 305) = P(Z > ( 305 - 303) / 5)

= P(Z > 0.4)

= 0.3446

b)

Using central limit theorem,

P( < x) = P(Z < ( x - ) / / sqrt(n) ) )

So,

P( < 302) = P(Z < ( 302. - 303 ) / (5 / sqrt(100) ))

= P(Z < -2)

= 0.0228

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