Question

The weight of potato chips in a largelarge​-size bag is stated to be 20 ounces. The...

The weight of potato chips in a largelarge​-size bag is stated to be 20 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 20.1 ounces and a standard deviation of 0.09 ounces. ​a) What fraction of all bags sold are​ underweight? ​b) Some of the chips are sold in​ "bargain packs" of 3 bags.​ What's the probability that none of the 3 is​ underweight? ​c) What's the probability that the mean weight of the 3 bags is below the stated​ amount? ​d) What's the probability that the mean weight of a 30-bag case of potato chips is below 20 ​ounces?

Given,

Mean = 20.1

Standard deviation = 0.09

a)

P(X < 20) = P((x-u)/s < (20 - 20.1)/0.09)

= P(z < -1.11)

= 0.1334995 [since from z table]

= 0.1335

b)

P(X > 20) = P((x-u)/(s/sqrt(n)) > (20 - 20.1)/(0.09/sqrt(3)))

= P(z > -1.92)

= 0.972571 [since from z table]

= 0.9726

c)

P(X < 20) = P((x-u)/(s/sqrt(n)) < (20 - 20.1)/(0.09/sqrt(3)))

= P(z < -1.92)

= 0.0274289 [since from z table]

= 0.0274

d)

P(X < 20) = P((x-u)/(s/sqrt(n)) < (20 - 20.1)/(0.09/sqrt(30)))

= P(z < -6.09)

= 0  [since from z table]

= 0