Question

Avalon Bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery $3.00 and can be sold for $6.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of 25, 50, and 75 loaves are 35%, 25%, and 40%, respectively. Make a recommendation for Avalon to bake 25, 50, or 75 loaves each morning.

Answer 1

Answer:

Answer #1

First question not clearly visible please re-post again

2)

Binomial probability

P(X = r) = nCr * P^r * q^n-r

Given n = 7, p = 0.65 and q = 1-p = 1-0.65 = 0.35

a)

P(X = 2) = 7C2 * 0.65^2 * 0.35^5 = 7!/2!(7−2)! * 0.4225 * 0.0053

P(X = 2) = 0.04660

b)

P(X ≤1) = P(X = 0) + P(X = 1)

P(X = 0) = 7C0 * 0.65^0 * 0.35^7 = 7!/0!(7−0)! * 1 * 0.00064 = 0.00064

P(X = 1) = 7C1 * 0.65^1 * 0.35^6 = 7!/1!(7−1)! * 0.65 * 0.0018 = 0.0084

P(X ≤1) = 0.00064 + 0.0084 = 0.0090

c)

P(X > 5) = P(X = 6)+P(X = 7)

P(X = 6) = 7C6 * 0.65^6 * 0.35^1 = 7!/6!(7−6)! * 0.0754 * 0.35 = 0.1848

P(X = 7) = 7C7 * 0.65^7 * 0.35^0 = 7!/7!(7−7)! * 0.0490 * 1 = 0.0490

P(X > 5) = 0.2338