The weight of a loaf of multi-grain bread that is sold in a local bakery has an

Question

The weight of a loaf of multi-grain bread that is sold in a local bakery has an average of 400 grams and a standard deviation of 5 grams. Due to product regulations, the bread is marked with a weight of 390 grams. Assume that the weights are normally distributed. Use this information and answer questions 3a to 3g. Question 3a What is the probability that a loaf of multi-grain bread sold by this local bakery weighs more than 402 grams? Question 3e: Assume that the original PDF for the weight of bread was given by the blue line marked as A. If you decided to improve the weight consistency of the bread, what would be the new weight probability density distribution function (PDF)? O D

Explanation / Answer

Answer to the question is as follows:

average = 400g

stdev = 5g

marked weight = 390g

3a. P(X>402)

= P(Z> 402-400 /5)

= P(Z> .4)

= 1-.6554

= .3446

3b. Like D, because the distribution will be more normal if you were to increase 'consistent'

In other words you are lessesing the deviation, by bringing in more consistency.

3c. P(X>=390)

= P(Z>= 390-400/5)

= P(Z>=-2)

= .9772

3d. If I want to do that, then I either i ) move the distribution to the right i.e. add more dough to each loaf of bread, or reduce variability of weight of the bed, so that distribution looks more normal. Therefore, 1st and 3rd are right.

3f. P(X>=400) = P(Z>= 400-408/10) = P(Z>=-0.8) =1-.2119 = .7881

3g. p( we bake cinamon bread) = 1/2 ( p(we bake multigrain bread)
p( we bake cinamon bread) +p( we bake multigrain bread) = 1
p( we bake cinamon bread) = 1/3, p( we bake multi grain bread)=2/3
Hence, a p(randomly selected load is multigrained and weights more than 390g) = p(you get multigrain)*
= 2/3 * (P(X>=390) = 2/3 * .9772 = .652

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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