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..... Which of the following normal curves corresponds to P(X> 37)? O A. В. 37 50 37 50 P(X>37) =| (Round to four decimal places as needed.)

..... Which of the following normal curves corresponds to P(X> 37)? O A. В. 37 50 37 50 P(X>37) =| (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
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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11-

### Standard Normal Distribution Table #### Overview This table presents values corresponding to the cumulative distribution function of the standard normal distribution. The values indicate the probability that a standard normal random variable \( Z \) will be less than or equal to a given value \( z \). The table is used extensively in statistical analysis for hypothesis testing and confidence interval estimation. #### Graph Explanation On the left, the graph of the standard normal distribution is shown. This bell-shaped curve represents a normal distribution with a mean of 0 and a standard deviation of 1. The shaded area under the curve to the left of a given \( z \) value represents the probability of obtaining a \( z \) less than that value. #### Table Structure - **Rows and Columns:** The table is organized by \( z \)-scores ranging from -3.4 to -2.0. - **Leftmost Column (\( z \)):** Lists the integral part of the \( z \)-scores and the first decimal place (e.g., -3.4, -3.3, …, -2.0). - **Top Row (Decimal Parts):** Shows the second decimal place ranging from .00 to .09. #### Example Usage To find the probability corresponding to a \( z \)-score of -2.57: 1. Locate the row for -2.5. 2. Move across to the column corresponding to .07. 3. The value at the intersection is 0.0051, indicating that there is a 0.51% probability that \( Z \) is less than -2.57. This table is a critical tool for determining probabilities and critical values in various statistical analyses.
Transcribed Image Text:### Standard Normal Distribution Table #### Overview This table presents values corresponding to the cumulative distribution function of the standard normal distribution. The values indicate the probability that a standard normal random variable \( Z \) will be less than or equal to a given value \( z \). The table is used extensively in statistical analysis for hypothesis testing and confidence interval estimation. #### Graph Explanation On the left, the graph of the standard normal distribution is shown. This bell-shaped curve represents a normal distribution with a mean of 0 and a standard deviation of 1. The shaded area under the curve to the left of a given \( z \) value represents the probability of obtaining a \( z \) less than that value. #### Table Structure - **Rows and Columns:** The table is organized by \( z \)-scores ranging from -3.4 to -2.0. - **Leftmost Column (\( z \)):** Lists the integral part of the \( z \)-scores and the first decimal place (e.g., -3.4, -3.3, …, -2.0). - **Top Row (Decimal Parts):** Shows the second decimal place ranging from .00 to .09. #### Example Usage To find the probability corresponding to a \( z \)-score of -2.57: 1. Locate the row for -2.5. 2. Move across to the column corresponding to .07. 3. The value at the intersection is 0.0051, indicating that there is a 0.51% probability that \( Z \) is less than -2.57. This table is a critical tool for determining probabilities and critical values in various statistical analyses.
Assume the random variable \( X \) is normally distributed with mean \( \mu = 50 \) and standard deviation \( \sigma = 7 \). Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. \[ P(X > 37) \] Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to \( P(X > 37) \)? - Option A - Option B - Option C \[ P(X > 37) = \] (Round to four decimal places as needed.) **Graphs Explanation:** - **Option A:** The normal curve is shown with shading from 37 to the right tail, indicating the area representing \( P(X > 37) \). - **Option B:** The normal curve is shown with shading from the left tail up to 37, indicating the area representing \( P(X < 37) \). - **Option C:** The normal curve is shown with shading only at the leftmost point beyond 37, indicating an incorrect shading for \( P(X > 37) \).
Transcribed Image Text:Assume the random variable \( X \) is normally distributed with mean \( \mu = 50 \) and standard deviation \( \sigma = 7 \). Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. \[ P(X > 37) \] Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to \( P(X > 37) \)? - Option A - Option B - Option C \[ P(X > 37) = \] (Round to four decimal places as needed.) **Graphs Explanation:** - **Option A:** The normal curve is shown with shading from 37 to the right tail, indicating the area representing \( P(X > 37) \). - **Option B:** The normal curve is shown with shading from the left tail up to 37, indicating the area representing \( P(X < 37) \). - **Option C:** The normal curve is shown with shading only at the leftmost point beyond 37, indicating an incorrect shading for \( P(X > 37) \).
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