b) Spacers are typically used in groups of four and tolerances require the total length of the 4 spacers to be between 155 mm and 165 mm. This means that the mean length of spacers in a pack has to be between 38.75 mm and 41.25 mm. The quality control officer for the company is looking at the likelihood of a pack of spacers being outside these tolerances. His interest shifts to the mean length of spacers in a sample of 4, which will be denoted X .i) State the distribution of the mean of a sample of 4 randomly selected spacers (that is, X ) and give the value(s) of its parameter(s). ii) Determine the probability that a randomly selected pack of spacers has a mean length that is inside the range 38.75 mm to 41.25 mm.

The total length of the 4 spacers to be between 155 mm and 165 mm. The mean length of spacers in a…

Answered: b) Spacers are typically used in…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

See similar textbooks

Related questions

Question

b) Spacers are typically used in groups of four and tolerances require the total length of the 4 spacers to be between 155 mm and 165 mm. This means that the mean length of spacers in a pack has to be between 38.75 mm and 41.25 mm. The quality control officer for the company is looking at the likelihood of a pack of spacers being outside these tolerances. His interest shifts to the mean length of spacers in a sample of 4, which will be denoted X .
i) State the distribution of the mean of a sample of 4 randomly selected spacers (that is, X ) and give the value(s) of its parameter(s).
ii) Determine the probability that a randomly selected pack of spacers has a mean length that is inside the range 38.75 mm to 41.25 mm.

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 + ...

Expert Solution