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(a) If X is a normal N(2,64) distribution, find k such that P(k ≤ X ≤12) = 0.2957 (b) The random variable T follows a t-distribution with 14 degrees of freedom. Find k such that P(-0.54

(a) If X is a normal N(2,64) distribution, find k such that P(k ≤ X ≤12) = 0.2957 (b) The random variable T follows a t-distribution with 14 degrees of freedom. Find k such that P(-0.54

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Question
(a) If X is a normal N(2,64) distribution, find k such that P(k ≤ X ≤12) = 0.2957 (b) The random variable T follows a t-distribution with 14 degrees of freedom. Find k such that P(-0.54 <T<k) = 0.3 (c) Six independent measurements are taken from a normal population. the sample has values x₁ = 4, x2 = 5, x3 = 8, x4 = 6, x5 = 5, x6 = 7. Find a 99% confidence interval for the mean. (d) The null hypothesis H, is a manufacturer's claim that a galvanized nail produced has averaged length μo = 2.5 inches. The alternative hypothesis H₁ that the nail length is μ₁μo. After testing a sample of 51 nails it is found that the sample average nail length is = 2.3 inches and that the sample standard deviation is s = 0.3 inches. For significance level a 1%, determine whether or not the manufacturer's claim should be accepted. Assume that the average nail length μ is uniformly distributed. =
Transcribed Image Text:(a) If X is a normal N(2,64) distribution, find k such that P(k ≤ X ≤12) = 0.2957 (b) The random variable T follows a t-distribution with 14 degrees of freedom. Find k such that P(-0.54 <T<k) = 0.3 (c) Six independent measurements are taken from a normal population. the sample has values x₁ = 4, x2 = 5, x3 = 8, x4 = 6, x5 = 5, x6 = 7. Find a 99% confidence interval for the mean. (d) The null hypothesis H, is a manufacturer's claim that a galvanized nail produced has averaged length μo = 2.5 inches. The alternative hypothesis H₁ that the nail length is μ₁μo. After testing a sample of 51 nails it is found that the sample average nail length is = 2.3 inches and that the sample standard deviation is s = 0.3 inches. For significance level a 1%, determine whether or not the manufacturer's claim should be accepted. Assume that the average nail length μ is uniformly distributed. =
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