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. 0.0174 b. 0.0228 c. 0.9826 d. 0.9772

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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)?

a.

0.0174

b.

0.0228

c.

0.9826

d.

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