A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. (i) The probability that a loaf of bread is between 20.75 and 23.25 ounces is 0.9876.
(ii. The probability that a loaf of bread is 21 ounces is 0.9772.
A) (i) and (ii) are correct statements.
B) (i) is a correct statement but not (ii).
C) (ii) is a correct statement but not (i).
D) (i) and (i) are false statements.

Question

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. (i) The probability that a loaf of bread is between 20.75 and 23.25 ounces is 0.9876.
(ii. The probability that a loaf of bread is > 21 ounces is 0.9772.
A) (i) and (ii) are correct statements.
B) (i) is a correct statement but not (ii).
C) (ii) is a correct statement but not (i).
D) (i) and (i) are false statements.

Quizplus · Accepted Answer

(i) Given the mean (μ) = 22 ounces and standard deviation (σ) = 0.5 ounces, the Z-scores for 20.75 and 23.25 ounces can be calculated. The Z-score for 20.75 is (20.75 - 22) / 0.5 = -2.5, and for 23.25 is (23.25 - 22) / 0.5 = 2.5. Looking at a standard normal distribution table, the area between Z = -2.5 and Z = 2.5 covers a significant portion of the curve, close to the probability stated. (ii) For a loaf greater than 21 ounces, the Z-score is (21 - 22) / 0.5 = -2. The probability to the right of Z = -2 is indeed high, aligning with the probability given.

A Loaf of Bread Is Normally Distributed with a Mean