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ply this customer? 5 Verify that P(|X-μ|> ko) = 2[1-(k)] for any k > 0 if X is N(u,0²) distributed. 5 Verify that aX + b is N(au + b, a²o2) distributed if X is N(u,0²) distributed. awart vlinsuport 1200 di to 15h

ply this customer? 5 Verify that P(|X-μ|> ko) = 2[1-(k)] for any k > 0 if X is N(u,0²) distributed. 5 Verify that aX + b is N(au + b, a²o2) distributed if X is N(u,0²) distributed. awart vlinsuport 1200 di to 15h

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
Section13.3: Special Probability Density Functions
Problem 8E
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Questions number 4.65 & 4.67

190 4 Continuous Random Variables 4.64 The lengths of steel beams made in a steel mill follow a normal distribution with an expected value of 10 m and a standard deviation of 0.07 m. A customer requires beams that are no shorter than 9.85 m and no longer than 10.15 m. What proportion of the mill's output can be used to supply this customer? todmun 1.65 Verify that P(X− µ| > ko) = 2[1-(k)] for any k > 0 if X is N(u,0²) distributed. .66 Verify that aX + b is N(au + b, a²o2) distributed if X is N(u,02) Unsuport 12nol ori distributed. 67 Somebody claims to have obtained 5,250 heads in 10,000 tosses of a fair coin. Do you believe this claim? 68 Let the random variable Z have the standard normal distribution. (a) Verify that the probability density function of |Z| is given by √2/1 e-² for z> 0 with E(Z) = √2/7 and o (Z))=√1-2/π. (6) TY
Transcribed Image Text:190 4 Continuous Random Variables 4.64 The lengths of steel beams made in a steel mill follow a normal distribution with an expected value of 10 m and a standard deviation of 0.07 m. A customer requires beams that are no shorter than 9.85 m and no longer than 10.15 m. What proportion of the mill's output can be used to supply this customer? todmun 1.65 Verify that P(X− µ| > ko) = 2[1-(k)] for any k > 0 if X is N(u,0²) distributed. .66 Verify that aX + b is N(au + b, a²o2) distributed if X is N(u,02) Unsuport 12nol ori distributed. 67 Somebody claims to have obtained 5,250 heads in 10,000 tosses of a fair coin. Do you believe this claim? 68 Let the random variable Z have the standard normal distribution. (a) Verify that the probability density function of |Z| is given by √2/1 e-² for z> 0 with E(Z) = √2/7 and o (Z))=√1-2/π. (6) TY
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Calculus For The Life Sciences
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ISBN:
9780321964038
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GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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