Question 3: The weight of a loaf of multi-grain bread that is sold in a local ba

Question

Question 3: 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 410 grams? Question 3b: Which area(s) under the curve represent the probability that a loaf of multi-grain bread is at least 405 grams? To receive full credit, please select all that apply.

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 400
standard Deviation ( sd )= 5
a.
P(X > 410) = (410-400)/5
= 10/5 = 2
= P ( Z >2) From Standard Normal Table
= 0.0228
b.
P(X < 405) = (405-400)/5
= 5/5= 1
= P ( Z <1) From Standard Normal Table
= 0.8413
P(X > = 405) = (1 - P(X < 405)
= 1 - 0.8413 = 0.1587
c.
P(X < 390) = (390-400)/5
= -10/5= -2
= P ( Z <-2) From Standard Normal Table
= 0.0228
P(X > = 390) = (1 - P(X < 390)
= 1 - 0.0228 = 0.9772
d.
option A, option B

f.
P(X < 400) = (400-400)/5
= 0/5= 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X > = 400) = (1 - P(X < 400)
= 1 - 0.5 = 0.5
g.
P(X > 390) = (390-400)/5
= -10/5 = -2
= P ( Z >-2) From Standard Normal Table
= 0.9772

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