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 ? 34% 34% 2.35% 2.35% 0.15% 13.5% 13.5% 0.15% de

There are two different values are provided for mean and standard deviation. I am using values given…

Answered: 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…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

The time to complete an exam is approximately Normal with a mean of 46 minutes and a standard deviation of 8 minutes.

The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.

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? [______] %

**Diagram Explanation:**

The diagram at the bottom of the image is a bell-shaped (normal) distribution curve. It is color-coded and labeled to represent the different percentages according to the Empirical Rule:

- The center of the distribution is labeled "x-bar" (mean), with each section representing standard deviations from the mean.
- The areas under the curve are divided as follows:
- Between -1s and +1s (one standard deviation from the mean): 34% on each side.
- Between -2s and -1s, and +1s and +2s (two standard deviations from the mean): 13.5% on each side.
- Between -3s and -2s, and +2s and +3s (three standard deviations from the mean): 2.35% on each side.
- Outside -3s and +3s: 0.15% on each side.

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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