Question

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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= 3 ml

What is the probability that an individual bottle contains less than 300 ml?

What is the probability that the sample mean of 80 bottles is less than 300 ml?

Answer 1

Solution :

Given that ,

mean = = 303

standard deviation = = 3

(a)

P(x < 300) = P((x - ) / < (300 - 303) / 3)

= P(z < -1)

= 0.1587

Probability = 0.1587

(b)

n = 80

= 303 and

= / n = 3 / 80 = 0.3354

P( < 300) = P(( - ) / < (300 - 303) / 0.3354)

= P(z < -8.94)

Using standard normal table,

Probability = 0