An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption that the claims are true, find the probability that a randomly selected battery of this type will last less than 48 months. (Use the software link for every question). : https://mathcracker.com/normal-probability-calculator-sampling-distributions Let X = number of months a battery will last. Write the question above in terms of this variable X P (x < 48)B) Find the probability that a single battery of this type will last less than 48 months. C) Find the probability that the mean of a random sample of 36 batterieswill be less than 48 months. D) Why do you think the values from part (b) and part (c) are different? Explain.

Write the question above in terms of this variable X as follows:X~μ,σ=50,6. B) Calculate the z score…

Answered: An automobile battery manufacturer…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption that the claims are true, find the probability that a randomly selected battery of this type will last less than 48 months. (Use the software link for every question). : https://mathcracker.com/normal-probability-calculator-sampling-distributions

Let X = number of months a battery will last. Write the question above in terms of this variable X

P (x < 48)

B) Find the probability that a single battery of this type will last less than 48 months.

C) Find the probability that the mean of a random sample of 36 batterieswill be less than 48 months.

D) Why do you think the values from part (b) and part (c) are different? Explain.

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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