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
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The time to complete an exam is approximately Normal with a
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F138bde95-779f-4adc-a9d5-2e50082ac839%2F6197d471-1b3b-466e-aa99-8bf2b4313312%2Fspkmffp_processed.jpeg&w=3840&q=75)
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