**Understanding Normal Distributions**The time to complete an exam is approximately normal with a mean of 55 minutes and a standard deviation of 7 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.- **Diagram Explanation**: The bell curve is a visual representation of a normal distribution. The center of the curve, labeled as \( \mu \), corresponds to the mean of the distribution (55 minutes). The horizontal axis represents deviations from the mean, calculated using the standard deviation (\( \sigma = 7 \)). The points along the axis are distributed as follows: - \( \mu - 3\sigma \) - \( \mu - 2\sigma \) - \( \mu - \sigma \) - \( \mu \) - \( \mu + \sigma \) - \( \mu + 2\sigma \) - \( \mu + 3\sigma \)- **Values to Fill**: - \( \mu - 3\sigma = 55 - 3 \times 7 = 34 \) - \( \mu - 2\sigma = 55 - 2 \times 7 = 41 \) - \( \mu - \sigma = 55 - 7 = 48 \) - \( \mu = 55 \) - \( \mu + \sigma = 55 + 7 = 62 \) - \( \mu + 2\sigma = 55 + 2 \times 7 = 69 \) - \( \mu + 3\sigma = 55 + 3 \times 7 = 76 \) These calculations allow for an understanding of how data is distributed across the standard deviation ranges from the mean in a normal distribution.

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Answered: Understanding Normal Distributions The…

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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Question Help Suppose you buy a new car whose advertised mileage is 20 miles per gallon (mpg). After driving your car for several months, you find that its mileage is 15.5 mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for all cars of the model you bought is 1.21 mpg. a. Find the z-score for the gas mileage of your car, assuming the advertised claim is correct. b. Does it appear that your car is getting unusually low gas mileage?
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Exam Scores An instructor gives a 100 -point examination in which the grades are normally distributed. The mean is 60 and the standard deviation is 7 . If there are 5% A 's and 5% F 's, 15% B 's and 15% D 's, and 60% C 's, find the scores that divide the distribution into those categories. Round the cutoff scores to the nearest whole number. Round intermediate z -value calculations to 2 decimal places. A: __- __B: __-__ C: __-__ D: __-__ F:__ -___
The area of the shaded region is
The time to complete an exam is approximately Normal with a mean of 41 minutes and a standard deviation of 7 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. µ = 41 o = 7 H- 30 u-20 µ-o u+o µ+20 µ+30
Indicated z score
Calculate the sample mean and sample standard deviation of the test scores. Test Scores Frequency 40 49 50 59 8 60 69 4 70 - 79 1 80 89 7 90 99 10 Round your answer to two decimal places. Mean = Standard Deviation = Question Help: D Video Check Answer Type here to search F1 F2 F3 F4 F5 F6 F7 F8 F9 #3 & 4. 7 8. W Y CO 立

The time to complete an exam is approximately Normal with a mean of 45 minutes and a standard deviation of 4 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.. μ-20 μισ μ-36 μ-20 μ μ+o μ=45 σ = 4 μ+20 μ+30
K Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Click to view page 1 of the table. Click to view page 2 of the table. The area of the shaded region is. (Round to four decimal places as needed.) C z = 0.89 Q a
Length of snowboards in a boardshop are normally distributed with a mean of 151.6 cm and a standard deviation of 0.7 cm. The figure below shows the distribution of the length of snowboards in a boardshop. Calculate the shaded area under the curve.Express your answer in decimal form accurate to at least two decimal places.

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