A bakery has determined that the number of loaves of its white bread demanded da

Question

A bakery has determined that the number of loaves of its white bread demanded daily has a Normal distribution with mean of 7, 200 loaves and standard deviation of 300 loaves. Based on cost considerations, the bakery has decided that its best strategy is to produce a sufficient number of loaves so that it will fully meet the demand on 94% of all days. a) How many loaves of bread the bakery should produce daily? b) Based on the answer in part (a), on what percentage of days will the bakery be left with more than 500 loaves of unsold bread?

Explanation / Answer

Let A be the number of loaves of bread to be produced daily

Given that P(X <A) = 0.94

Mean = 7200

Standard deviation = 300

P(X < A) = P(Z < (A - mean)/standard deviation)

So, P(Z < (A - 7200)/300) = 0.94

From standard normal distribution table,

(A - 7200)/300 = 1.555

A = 7666.5

So, number of loaves to be produced = 7667

b) More lan 500 loaves unsolved means, demand was less than 7667-500 = 7167

P(X < 7167) = P(Z < (7167 - 7200)/300)

= P(Z < -0.11)

= 0.4562

So, on 45.62% days, the bakery will be left with more than 500 loaves of unsold bread

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.