Central Limit Theorem: The Rockwell hardness of certain metal pins is known to have a mean of 50 and a stan- dard deviation of 1.5 (Round your answers to 4 decimal places). (a) If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the mean hardness for a random sample of 9 pins is at least 52? (a). (b) What is the approximate probability that the mean hard- a random sample of 40 pins is at least 52? ness (b).

Central Limit Theorem: The Rockwell hardness of certain metal pins is known to have a mean of 50 and a stan- dard deviation of 1.5 (Round your answers to 4 decimal places). (a) If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the mean hardness for a random sample of 9 pins is at least 52? (a). (b) What is the approximate probability that the mean hard- a random sample of 40 pins is at least 52? ness (b).

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

**Central Limit Theorem:** The Rockwell hardness of certain metal pins is known to have a mean of 50 and a standard deviation of 1.5 *(Round your answers to 4 decimal places).*

(a) If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the mean hardness for a random sample of 9 pins is at least 52?

(a) ____________

(b) What is the approximate probability that the mean hardness in a random sample of 40 pins is at least 52?

(b) ____________

*Image description:* The image contains a picture of a hardness testing machine used to measure the Rockwell hardness of metal pins.

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