**The Acme Company manufactures widgets.** The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 ounces.**Use the Standard Deviation Rule, also known as the Empirical Rule.** *(See image below)*. Do not use normalcdf on your calculator.**Suggestion:** Sketch the distribution in order to answer these questions.a) **99.7% of the widget weights lie between** [______] **and** [______].b) **What percentage of the widget weights lie between 18 and 68 ounces?** [______]%c) **What percentage of the widget weights lie above 28?** [______]%---**Explanation of Diagram:**The diagram at the bottom of the image is a bell curve (normal distribution) illustrating the Empirical Rule:- The central line is labeled as "x-bar" (mean), at 38 ounces.- The shaded areas represent the distribution of data around the mean: - 34% of data lies within one standard deviation (10 ounces) to the left or right of the mean. - 13.5% lies between one and two standard deviations from the mean. - 2.35% lies between two and three standard deviations from the mean. - 0.15% lies beyond three standard deviations on either side.

It is given that the mean is 38 and the standard deviation is 10.

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 18 and 68 ounces? c) What percentage of the widget weights lie above 28 ?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 18 and 68 ounces? c) What percentage of the widget weights lie above 28 ?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

**The Acme Company manufactures widgets.**

The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 ounces.

**Use the Standard Deviation Rule, also known as the Empirical Rule.**

*(See image below)*. Do not use normalcdf on your calculator.

**Suggestion:** Sketch the distribution in order to answer these questions.

a) **99.7% of the widget weights lie between** [______] **and** [______].

b) **What percentage of the widget weights lie between 18 and 68 ounces?** [______]%

c) **What percentage of the widget weights lie above 28?** [______]%

---

**Explanation of Diagram:**

The diagram at the bottom of the image is a bell curve (normal distribution) illustrating the Empirical Rule:

- The central line is labeled as "x-bar" (mean), at 38 ounces.
- The shaded areas represent the distribution of data around the mean:
- 34% of data lies within one standard deviation (10 ounces) to the left or right of the mean.
- 13.5% lies between one and two standard deviations from the mean.
- 2.35% lies between two and three standard deviations from the mean.
- 0.15% lies beyond three standard deviations on either side.

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