Disc Brake pads has a Normal distribution with a mean µ = 50,000 miles but with some unknown standard deviation σ . In a sample of n =16 pads is tested for their ‘life-times’ yield S = 2500 as the sample estimate σ . What is the probability that the sample average X16 exceeds 49,000 miles, Pr( 49,000)=_________ Suppose that the 'life-time' of Disc Brake pads has a Normal distribution with amean = 50,000 miles but with some unknown standard deviation σ. Supposethat a sample of n = 16 pads is tested for their 'life-times' yield S = 2500 as thesample estimate σ. Find the probability that the sample average X16 exceeds49,000 miles,Pr(≥49,000)16

Step 1 : Given Information:The lifetime of disc brake pads follows a Normal distribution with a mean…

Answered: Suppose that the 'life-time' of Disc…

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

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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Disc Brake pads has a Normal distribution with a mean µ = 50,000 miles but with some unknown standard deviation σ . In a sample of n =16 pads is tested for their ‘life-times’ yield S = 2500 as the
sample estimate σ . What is the probability that the sample average X16 exceeds
49,000 miles,
Pr( 49,000)=_________

Suppose that the 'life-time' of Disc Brake pads has a Normal distribution with a
mean = 50,000 miles but with some unknown standard deviation σ. Suppose
that a sample of n = 16 pads is tested for their 'life-times' yield S = 2500 as the
sample estimate σ. Find the probability that the sample average X16 exceeds
49,000 miles,
Pr(≥49,000)
16

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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