The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. A random sample of 36 cars is selected.What is the standard error of the mean?What is the probability that the sample mean is between 40 and 50 minutes?What is the probability that the sample mean will be between 35 and 48 minutes?95% of all sample means will fall between which two values? please write formulas as well

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Answered: The amount of time required for an oil…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. A random sample of 36 cars is selected.

What is the standard error of the mean?
What is the probability that the sample mean is between 40 and 50 minutes?
What is the probability that the sample mean will be between 35 and 48 minutes?
95% of all sample means will fall between which two values?

please write formulas as well

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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