Given a normal distribution with μ= 105 and σ = 20, and given you select a sample of n = 16, complete parts (a) through (d). a. What is the probability that X is less than 92? P(X<92) 0.0047 (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X is between 92 and 93.5? P(92 X 93.5)= 0.0061 (Type an integer or decimal rounded to four decimal places as needed.) c. What is the probability that X is above 105.2? P(X 105.2)= 0.4840 (Type an integer or decimal rounded to four decimal places as needed.) d. There is a 67% chance that X is above what value? X = (Type an integer or decimal rounded to two decimal places as needed.)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter14: Data Mining
Section14.2: Classification Methods
Problem 11P
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Given a normal distribution with μ= 105 and σ = 20, and given you select a sample of n = 16, complete parts (a)
through (d).
a. What is the probability that X is less than 92?
P(X<92)
0.0047
(Type an integer or decimal rounded to four decimal places as needed.)
b. What is the probability that X is between 92 and 93.5?
P(92 X 93.5)= 0.0061
(Type an integer or decimal rounded to four decimal places as needed.)
c. What is the probability that X is above 105.2?
P(X 105.2)= 0.4840
(Type an integer or decimal rounded to four decimal places as needed.)
d. There is a 67% chance that X is above what value?
X =
(Type an integer or decimal rounded to two decimal places as needed.)
Transcribed Image Text:Given a normal distribution with μ= 105 and σ = 20, and given you select a sample of n = 16, complete parts (a) through (d). a. What is the probability that X is less than 92? P(X<92) 0.0047 (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X is between 92 and 93.5? P(92 X 93.5)= 0.0061 (Type an integer or decimal rounded to four decimal places as needed.) c. What is the probability that X is above 105.2? P(X 105.2)= 0.4840 (Type an integer or decimal rounded to four decimal places as needed.) d. There is a 67% chance that X is above what value? X = (Type an integer or decimal rounded to two decimal places as needed.)
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