Question

The chocolate factory "Charlie’s own" produces limited-time boxes with exactly 9 chocolates. The research department of the factory models the weight of a chocolate by the random variable X, with expected value E(X) = 5 and variance Var(X) = 0.09. Customers who buy a box with chocolate weight less than 42.75 are reimbursed and given a coupon for their next purchase. Give an estimate of the percentage of boxes with weight less than 42.75. Leave your answer in terms of Φ, the distribution function of a standard normal random variable.

Answer 1

Answer:

Step-by-step explanation:

Given that the chocolate factory "Charlie’s own" produces limited-time boxes with exactly 9 chocolates.

X is the weight of chocolate

X is N (5, 0.3) (since variance = 0.09, std dev  =sqrt of variance = 0.3)

Probability for the box to weight <42.75 =

P(X<42.75)

=$P(Z<\frac{42.75-5(9)}{3(0.3)} =P(Z<-2.5)\\=0.5-0.4938\\=0.0062$

Or 0.62% of boxed weigh <42.75

$\phi = -2.5$