Question

1 point) The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 8.2 ounces and standard deviation 0.12 ounces.

(a) What is the probability that the average weight of a bar in a Simple Random Sample (SRS) with three of these chocolate bars is between 8.06 and 8.34 ounces?
ANSWER:

(b) For a SRS of three of these chocolate bars, what is the level LL such that there is a 2% chance that the average weight is less than LL?

Answer 1

Solution:-

a) The probability that the average weight of a bar in a Simple Random Sample (SRS) with three of these choclate bars is between 8.06 and 8.34 ounces is  0.758.

x₁ = 8.06

x₂ = 8.34

By applying normal distruibution:-

z₁ = - 1.17

z₂ = 1.17

P( - 1.17 < z < 1.17) = P(z > - 1.17) - P(z > 1.17)

P( - 1.17 < z < 1.17) = 0.879 - 0.121

P( - 1.17 < z < 1.17) = 0.758

b) The level LL such that there is a 2% chance that the average weight is less than LL is 7.954.

p-value for the bottom 2% = 0.02

z-score for the p-value = - 2.054

By applying normal distruibution:-

x = 7.954