Question

Question#: 13 Question: The mean weight for crates of apples are normally distributed with a mean weight of 34.6 pounds and a standard deviation of 2.8 pounds. Considering 75 crates of apples, what is the probability that the mean weight is between 31 and 35 pounds? Options: a) 0.8925 b)0.1075 c)0.4572 d)0.7843 Correct Answer: a Question#: 14 Question: The mean weight for crates of apples are normally distributed with a mean weight of 34.6 pounds and a standard deviation of 2.8 pounds. Considering 40 crates of apples, what is the probability that the mean weight is less than 33.5 pounds? Options: a) 0.0007 b)0.0066 c)0.3483 d)0.3583 Correct Answer: b

Answer 1

Answer 13

mean, mu= 34.6 pounds

standard deviation, sigma= 2.8 pounds

sample size, n= 75

P(31 < mean weight < 35)= P(mean weight < 35) - P(mean weight < 31)

= P(Z < (35-34.6)/2.8/sqrt(75)) - P(Z < (31-34.6)/2.8/sqrt(75))

= P(Z < (0.4)/0.32331615074) - P(Z < (-3.6)/0.32331615074)

= P(Z < 1.23717914829) - P(Z < -11.1346123346)

= 0.8925 - 0

= 0.8925

Thus, the correct answer is option a.

Answer 14

mean, mu= 34.6 pounds

standard deviation, sigma= 2.8 pounds

sample size, n= 40

P(mean weight < 33.5)= P(Z < (33.5-34.6)/2.8/sqrt(40))

= P(Z < (-1.1)/0.44271887242)

= P(Z < -2.48464673301)

= 0.0066

Thus, the correct answer is option b.