Math 227 - Statistics » Spring 2023 » 12KC Assessing Normality & Normal as Approximation to Binomial

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Question #1
Acme's widgets have a defect rate of 3%. Find the probability that 4 widgets are broken in a 12-pack? (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.0003
B.   0.0004
C.   0.0002
D.   0.0001
Question #2
Acme's widgets have a defect rate of 3%. What is the probability that more than 2 widgets are broken in a 12-pack? (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.0036
B.   0.0038
C.   0.0048
D.   0.0044
Question #3
Acme's widgets have a defect rate of 3%. Would 3 broken widgets in a 12-pack be significantly high?
A.   3 broken widgets in a 12-pack would NOT be significantly high because the probability of 3 or more successes is NOT 0.05 or less.
B.   3 broken widgets in a 12-pack would be significantly high because the probability of 3 or more successes is NOT 0.05 or less.
C.   3 broken widgets in a 12-pack would NOT be significantly high because the z-score of 3 is NOT between -2 and 2.
D.   3 broken widgets in a 12-pack would NOT be significantly high because the probability of 3 or fewer successes is 0.05 or less.
E.   3 broken widgets in a 12-pack would be significantly high because the z-score of 3 is NOT between -2 and 2.
F.   3 broken widgets in a 12-pack would be significantly high because the probability of 3 or more successes is 0.05 or less.
Question #4
Acme's widgets have a defect rate of 3%. Find the standard deviation for the number of widgets that are broken in a 12-pack? (Round to the nearest ten-thousandth.)
A.   0.5909
B.   0.5819
C.   0.4809
D.   0.5627
Question #5
Acme's widgets have a defect rate of 3%. Would it be unusual to purchase a 12-pack containing 3 broken widgets?
A.   Purchasing a 12-pack containing 3 broken widgets is unusual because the probability of 3 or more successes is 0.05 or less.
B.   Purchasing a 12-pack containing 3 broken widgets is NOT unusual because the probability of 3 or more successes is 0.05 or less.
C.   Purchasing a 12-pack containing 3 broken widget is NOT unusual because the probability of 3 or fewer successes is NOT 0.05 or less.
D.   Purchasing a 12-pack containing 3 broken widget is unusual because the probability of 3 or fewer successes is 0.05 or less.
E.   Purchasing a 12-pack containing 3 broken widgets is unusual because the probability of 3 or more successes is NOT 0.05 or less.
F.   Purchasing a 12-pack containing 3 broken widget is unusual because the z-score of 3 is NOT between -2 and 2.
Question #6
Acme's widgets have a defect rate of 3%. When dealing with a 200-pack, may probabilities for the number of broken widgets be approximated/estimated using the Poisson Distribution? Why, or why not?
A.   Both of the requirements are NOT met! The Poisson Distribution cannot be used to approximate the Binomial Disribution. np≥5 is a true statement. np≤10 is a true statement.
B.   np≤10 is a true statement. n≥100 is a true statement. Both of the requirements are met! The mean of the Binomial Distribution may be used for Poisson Distribution calculations.
C.   Both of the requirements are NOT met! The Poisson Distribution cannot be used to approximate the Binomial Disribution. n≥100 is NOT a true statement. nq≥5 is a true statement.
D.   np≥5 is NOT a true statement. np≤10 is NOT a true statement. Both of the requirements are NOT met! The Poisson Distribution cannot be used to approximate the Binomial Disribution.
Question #7
Acme's widgets have a defect rate of 3%. When dealing with a 200-pack, may probabilities for the number of broken widgets be approximated/estimated using the Normal Distribution? Why, or why not?
A.   Both of the requirements are met! The mean and standard deviation of the Binomial Distribution may be used for Normal Distribution calculations. nq≥5 is a true statement. np≥5 is a true statement.
B.   Both of the requirements are NOT met! The Normal Distribution cannot be used to approximate the Binomial Disribution. n≥100 is a true statement. n≥100 is NOT a true statement.
C.   n≥100 is a true statement. np≤10 is NOT a true statement. Both of the requirements are NOT met! The Normal Distribution cannot be used to approximate the Binomial Disribution.
D.   Both of the requirements are NOT met! The Normal Distribution cannot be used to approximate the Binomial Disribution. nq≥5 is NOT a true statement. np≥5 is NOT a true statement.
Question #8
Acme's widgets have a defect rate of 3%. Find the standard deviation for the number of widgets that are broken in a 200-pack? (Round to the nearest ten-thousandth.)
A.   2.4125
B.   2.1125
C.   3.4125
D.   2.2122
Question #9
Acme's widgets have a defect rate of 3%. Find the probability that 8 widgets are broken in a 200-pack using the Binomial Distribution. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.1043
B.   0.1085
C.   0.1185
D.   0.1033
Question #10
Acme's widgets have a defect rate of 3%. Approximate/estimate the probability that 8 widgets are broken in a 200-pack using the Poisson Distribution. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.1033
B.   0.1088
C.   0.1055
D.   0.1133
Question #11
Acme's widgets have a defect rate of 3%. Approximate/estimate the probability that 8 widgets are broken in a 200-pack using the Normal Distribution. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.137
B.   0.117
C.   0.127
D.   0.129
Question #12
Acme's widgets have a defect rate of 3%. When dealing with a 400-pack, may probabilities for the number of broken widgets be approximated/estimated using the Poisson Distribution? Why, or why not?
A.   np≤10 is NOT a true statement. n≥100 is a true statement. Both of the requirements are NOT met! The Poisson Distribution cannot be used to approximate the Binomial Disribution.
B.   Both of the requirements are met! The mean of the Binomial Distribution may be used for Poisson Distribution calculations. np≤10 is a true statement nq≥5 is NOT a true statement.
C.   nq≥5 is a true statement. Both of the requirements are met! The mean of the Binomial Distribution may be used for Poisson Distribution calculations. n≥100 is NOT a true statement.
D.   np≥5 is NOT a true statement. np≥5 is a true statement. Both of the requirements are met! The mean of the Binomial Distribution may be used for Poisson Distribution calculations.
Question #13
Acme's widgets have a defect rate of 3%. When dealing with a 400-pack, may probabilities for the number of broken widgets be approximated/estimated using the Normal Distribution? Why, or why not?
A.   np≥5 is a true statement. Both of the requirements are met! The mean and standard deviation of the Binomial Distribution may be used for Normal Distribution calculations. nq≥5 is a true statement.
B.   Both of the requirements are NOT met! The Normal Distribution cannot be used to approximate the Binomial Disribution. n≥100 is a true statement. nq≥5 is NOT a true statement.
C.   np≤10 is NOT a true statement. np≥5 is NOT a true statement. Both of the requirements are NOT met! The Normal Distribution cannot be used to approximate the Binomial Disribution.
D.   Both of the requirements are NOT met! The Normal Distribution cannot be used to approximate the Binomial Disribution. n≥100 is NOT a true statement. np≤10 is a true statement.
Question #14
Acme's widgets have a defect rate of 3%. Find the standard deviation for the number of widgets that are broken in a 400-pack? (Round to the nearest ten-thousandth.)
A.   3.3322
B.   3.5123
C.   3.4117
D.   3.4219
Question #15
Acme's widgets have a defect rate of 3%. Approximate/estimate the probability that between 5 and 18 widgets are broken in a 400-pack. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.9156
B.   0.9181
C.   0.8517
D.   0.9388
Question #16
STATDISK has the ability to test for normality using the normal quantile plot. The next question is designed to introduce you to this functions within STATDISK. For more information, please review the following tutorial. Always feel free to pause and/or restart the video. Load the data set "AMATYC-NASA"--"Distance Moon-Earth" into STATDISK. Assess the normality of the "Distance" column data.
A.   The normality assessment concludes that normality should fail to be rejected.
B.   The normality assessment concludes that normality should be rejected.

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