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[10] The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30, 16). Let T = Y+3. a) Compute E(T) and Var(T). What is the distribution of T? in general knowing the expected value and variance doesn't mean that we know the distribution, but when Y is normal, T will be normal as well because T is basically scaling and then shifting Y so its shape is not going to change. Indeed, the standard Z-transformation does something similar.) b) Can you compute the following probability P(8.5 ≤ T ≤ 10)? Explain why. c) Compute P(T> 21)? d) Compute P(14 ≤ T ≤ 20)?

[10] The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30, 16). Let T = Y+3. a) Compute E(T) and Var(T). What is the distribution of T? in general knowing the expected value and variance doesn't mean that we know the distribution, but when Y is normal, T will be normal as well because T is basically scaling and then shifting Y so its shape is not going to change. Indeed, the standard Z-transformation does something similar.) b) Can you compute the following probability P(8.5 ≤ T ≤ 10)? Explain why. c) Compute P(T> 21)? d) Compute P(14 ≤ T ≤ 20)?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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[10] The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30, 16). Let T = Y+3. a) Compute E(T) and Var(T). What is the distribution of T? in general knowing the expected value and variance doesn't mean that we know the distribution, but when Y is normal, T will be normal as well because T is basically scaling and then shifting Y so its shape is not going to change. Indeed, the standard Z-transformation does something similar.) b) Can you compute the following probability P(8.5 ≤ T≤ 10)? Explain why. c) Compute P(T > 21)? d) Compute P(14 ≤ T ≤ 20)?
Transcribed Image Text:[10] The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30, 16). Let T = Y+3. a) Compute E(T) and Var(T). What is the distribution of T? in general knowing the expected value and variance doesn't mean that we know the distribution, but when Y is normal, T will be normal as well because T is basically scaling and then shifting Y so its shape is not going to change. Indeed, the standard Z-transformation does something similar.) b) Can you compute the following probability P(8.5 ≤ T≤ 10)? Explain why. c) Compute P(T > 21)? d) Compute P(14 ≤ T ≤ 20)?
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