The time required for a citizen to complete a 2000 U.S. Census “long” form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What is the probability that a citizen will need more than 60 minutes to complete a “long” form (using the partial Appendix C-2 table below)?a.0.0174b.0.0228c.0.9826d.0.9772 The image is a table representing the probability values for a standard normal distribution, often referred to as a Z-table. It shows the cumulative probabilities \( P(Z < z) \) for specific Z-scores.The columns represent the decimal part of the Z-score: 0.00, 0.01, and 0.02. The rows represent the integer and first decimal of the Z-score: 1.8, 1.9, 2.0, and 2.1.Here's the table breakdown:- For \( Z = 1.8 \): - \( P(Z < 1.80) = 0.9641 \) - \( P(Z < 1.81) = 0.9649 \) - \( P(Z < 1.82) = 0.9656 \)- For \( Z = 1.9 \): - \( P(Z < 1.90) = 0.9713 \) - \( P(Z < 1.91) = 0.9719 \) - \( P(Z < 1.92) = 0.9726 \)- For \( Z = 2.0 \): - \( P(Z < 2.00) = 0.9772 \) - \( P(Z < 2.01) = 0.9778 \) - \( P(Z < 2.02) = 0.9783 \)- For \( Z = 2.1 \): - \( P(Z < 2.10) = 0.9821 \) - \( P(Z < 2.11) = 0.9826 \) - \( P(Z < 2.12) = 0.9830 \)

X~N( μ , ?)μ=40 , ?=10Z-score =( x - μ )/?

Answered: The time required for a citizen to…

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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The time required for a citizen to complete a 2000 U.S. Census “long” form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What is the probability that a citizen will need more than 60 minutes to complete a “long” form (using the partial Appendix C-2 table below)?

0.0174

0.0228

0.9826

0.9772

The image is a table representing the probability values for a standard normal distribution, often referred to as a Z-table. It shows the cumulative probabilities \( P(Z < z) \) for specific Z-scores.

The columns represent the decimal part of the Z-score: 0.00, 0.01, and 0.02. The rows represent the integer and first decimal of the Z-score: 1.8, 1.9, 2.0, and 2.1.

Here's the table breakdown:

- For \( Z = 1.8 \):
- \( P(Z < 1.80) = 0.9641 \)
- \( P(Z < 1.81) = 0.9649 \)
- \( P(Z < 1.82) = 0.9656 \)

- For \( Z = 1.9 \):
- \( P(Z < 1.90) = 0.9713 \)
- \( P(Z < 1.91) = 0.9719 \)
- \( P(Z < 1.92) = 0.9726 \)

- For \( Z = 2.0 \):
- \( P(Z < 2.00) = 0.9772 \)
- \( P(Z < 2.01) = 0.9778 \)
- \( P(Z < 2.02) = 0.9783 \)

- For \( Z = 2.1 \):
- \( P(Z < 2.10) = 0.9821 \)
- \( P(Z < 2.11) = 0.9826 \)
- \( P(Z < 2.12) = 0.9830 \)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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