Question

Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams.

If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?
(A) It is extremely unlikely for this to occur; the probability is very close to 0.
(B) There is about a 5% chance of this occurring.
(C) There is about a 16% chance of this occurring.
(D) There is no way to evaluate this likelihood, since the sample size (n = 4) is too small.
(E) There is about a 2.5% chance of this occurring.

Answer 1

Explanation:

Given that the weight of a candy bar X is N(mean = 50 gm, 2 = sigma)

Packs of 4 bars

n = sample size = 4

Std error of sample = sigma/sqrt n = 1

P(Mean diff > 4 gms) = P(Z>4/Se ) = P(Z>4)

=0.0000

Hence it is an impossible event

Option A

(A) It is extremely unlikely for this to occur; the probability is very close to 0.