Question

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?

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