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Assume the random variable X is normally distributed with mean u = 50 and standard deviation o = 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(53 SXS67) E Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to P(53 sXS67)? OA. OB. Oc. 50 53 67 50 53 67 50 53 67 P(53 sXs67) = (Round to four decimal places as needed.)

Assume the random variable X is normally distributed with mean u = 50 and standard deviation o = 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(53 SXS67) E Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to P(53 sXS67)? OA. OB. Oc. 50 53 67 50 53 67 50 53 67 P(53 sXs67) = (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
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**Normal Distribution Probability Calculation** 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(53 ≤ X ≤ 67)** \[ \text{Click the icon to view a table of areas under the normal curve.} \] --- **Which of the following normal curves corresponds to P(53 ≤ X ≤ 67)?** - **Option A**: Diagram shows a normal distribution curve with the mean at 50. The shaded region spans from 53 to 67 on the x-axis, starting slightly to the right of the mean and extending to the right tail of the curve. - **Option B**: Diagram shows a normal distribution curve with the shaded area between 50 and 53, excluding 67. - **Option C**: Diagram shows a normal distribution curve with the shaded area between 50 and 67, excluding 53. --- **\[ \text{P(53 ≤ X ≤ 67) = } \]** [Round to four decimal places as needed.] The correct diagram representing the probability is **Option A**, where the area under the curve between 53 and 67 is shaded.
Transcribed Image Text:**Normal Distribution Probability Calculation** 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(53 ≤ X ≤ 67)** \[ \text{Click the icon to view a table of areas under the normal curve.} \] --- **Which of the following normal curves corresponds to P(53 ≤ X ≤ 67)?** - **Option A**: Diagram shows a normal distribution curve with the mean at 50. The shaded region spans from 53 to 67 on the x-axis, starting slightly to the right of the mean and extending to the right tail of the curve. - **Option B**: Diagram shows a normal distribution curve with the shaded area between 50 and 53, excluding 67. - **Option C**: Diagram shows a normal distribution curve with the shaded area between 50 and 67, excluding 53. --- **\[ \text{P(53 ≤ X ≤ 67) = } \]** [Round to four decimal places as needed.] The correct diagram representing the probability is **Option A**, where the area under the curve between 53 and 67 is shaded.
**Standard Normal Distribution Table** The image displays a standard normal distribution curve along with a table labeled "Table V." This table provides critical values for the standard normal distribution, used frequently in statistics for finding probabilities associated with a standard normal random variable, \( z \). **Diagram Explanation:** - The diagram on the left shows a standard normal distribution curve, which is bell-shaped and symmetric. - An area under the curve is shaded, representing the probability of the random variable falling within that range. - The z-score, denoted by \( z \), is marked on the horizontal axis, indicating the distance from the mean in terms of standard deviations. **Table Explanation:** The table lists z-scores and their corresponding probabilities for various decimal places, ranging from \( z = -3.4 \) to \( z = 3.7 \). The z-scores are divided into two components: the row (integer and first decimal place) and the column (second decimal place). - **Columns**: Indicate the second decimal place of the z-score (from .00 to .09). - **Rows**: Indicate the z-score from -3.4 to 3.7. Each cell intersection provides the cumulative probability from the left up to the specified z-score. For example: - A z-score of -1.5 with a second decimal place of .06 is found in the row marked -1.5 and the column .06, giving a probability of 0.0594. - A z-score of 0.5 with a second decimal place of .02 is found in the row marked 0.5 and the column .02, resulting in a probability of 0.6915. The table is crucial for statistical analyses, allowing users to determine the likelihood of z-scores occurring in a standard normal distribution.
Transcribed Image Text:**Standard Normal Distribution Table** The image displays a standard normal distribution curve along with a table labeled "Table V." This table provides critical values for the standard normal distribution, used frequently in statistics for finding probabilities associated with a standard normal random variable, \( z \). **Diagram Explanation:** - The diagram on the left shows a standard normal distribution curve, which is bell-shaped and symmetric. - An area under the curve is shaded, representing the probability of the random variable falling within that range. - The z-score, denoted by \( z \), is marked on the horizontal axis, indicating the distance from the mean in terms of standard deviations. **Table Explanation:** The table lists z-scores and their corresponding probabilities for various decimal places, ranging from \( z = -3.4 \) to \( z = 3.7 \). The z-scores are divided into two components: the row (integer and first decimal place) and the column (second decimal place). - **Columns**: Indicate the second decimal place of the z-score (from .00 to .09). - **Rows**: Indicate the z-score from -3.4 to 3.7. Each cell intersection provides the cumulative probability from the left up to the specified z-score. For example: - A z-score of -1.5 with a second decimal place of .06 is found in the row marked -1.5 and the column .06, giving a probability of 0.0594. - A z-score of 0.5 with a second decimal place of .02 is found in the row marked 0.5 and the column .02, resulting in a probability of 0.6915. The table is crucial for statistical analyses, allowing users to determine the likelihood of z-scores occurring in a standard normal distribution.
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