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The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=(x-1)²(4-x) for 1 ≤ x ≤ 4 and 0 otherwise. a) What is the probability that X > 2.5?¹ b) What is the probability that X < 2.572 c) What is the probability that 1.25 < X < 2.75? d) What is the expected value of X? 4 e) What is the expected value of X-3? 6 f) What is the expected value of 3X? 9) What is the expected value of x27 h) What is the probability that X is less than its expected value? 8

The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=(x-1)²(4-x) for 1 ≤ x ≤ 4 and 0 otherwise. a) What is the probability that X > 2.5?¹ b) What is the probability that X < 2.572 c) What is the probability that 1.25 < X < 2.75? d) What is the expected value of X? 4 e) What is the expected value of X-3? 6 f) What is the expected value of 3X? 9) What is the expected value of x27 h) What is the probability that X is less than its expected value? 8

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=(x − 1)²(4 - x) for 1 ≤ x ≤ 4 and 0 otherwise. 27 1 a) What is the probability that X > 2.5? 2 b) What is the probability that X < 2.5? c) What is the probability that 1.25 < X < 2.75? d) What is the expected value of X? 4 e) What is the expected value of X - 3? 5 f) What is the expected value of 3X? 7 g) What is the expected value of x²? h) What is the probability that X is less than its expected value? i) What is the expected value of √X?! 9 8 j) What is the 70th percentile of X? 10 k) What is the probability that X is within 0.1 of its expected value? 11 1) What is the probability that X = 0.7? 12
Transcribed Image Text:The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=(x − 1)²(4 - x) for 1 ≤ x ≤ 4 and 0 otherwise. 27 1 a) What is the probability that X > 2.5? 2 b) What is the probability that X < 2.5? c) What is the probability that 1.25 < X < 2.75? d) What is the expected value of X? 4 e) What is the expected value of X - 3? 5 f) What is the expected value of 3X? 7 g) What is the expected value of x²? h) What is the probability that X is less than its expected value? i) What is the expected value of √X?! 9 8 j) What is the 70th percentile of X? 10 k) What is the probability that X is within 0.1 of its expected value? 11 1) What is the probability that X = 0.7? 12
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