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d) Theth percentile corresponds to this score, which means that 299 is (Round to five decimal places as needed.) than % of all his other scores.

d) Theth percentile corresponds to this score, which means that 299 is (Round to five decimal places as needed.) than % of all his other scores.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 4CYU
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### Understanding the Z-Table The table provided is commonly known as a Z-table and is used in statistics to determine the area (or probability) under the normal curve up to a given z-score. The z-score represents the number of standard deviations a data point is from the mean of a distribution. This table is especially useful for finding cumulative probabilities in a standard normal distribution. #### Description of the Table - **Columns and Rows**: - The first column (`Z`) lists z-scores from 0.0 to 3.0 in increments of 0.1. - The remaining columns provide additional precision by listing the probability values for increments of 0.01 from 0.00 to 0.09. - **Entries**: - Each entry in the table gives the probability that a standard normal variable will fall below the given z-score. - For example, to find the area under the curve to the left of z = 1.23, locate the row for `z = 1.2` and the column `0.03`. The intersecting value, 0.8907, is the area under the normal curve to the left of z = 1.23. #### How to Use the Table 1. **Locate z-score**: Identify the z-score for which you want to find the cumulative probability. For example, if you have a z-score of 1.25: - Find the row corresponding to the z-score's integer and first decimal place (`1.2`). - Find the column corresponding to the hundredths place (`0.05`). 2. **Find the Probability**: - Intersection of the row and column provides the cumulative probability up to that z-score. #### Working with Negative Z-Scores Due to the symmetry of the normal distribution curve: - For a negative z-score, simply find the positive z-score and subtract the table value from 1. - For example, to find the area to the left of z = -1.25: - Locate the value for z = 1.25 (0.8944). - Subtract it from 1: \(1 - 0.8944 = 0.1056\). ### Table Example Explained ``` Z 0.00 0.01 0.02 0.03 0.04
Transcribed Image Text:### Understanding the Z-Table The table provided is commonly known as a Z-table and is used in statistics to determine the area (or probability) under the normal curve up to a given z-score. The z-score represents the number of standard deviations a data point is from the mean of a distribution. This table is especially useful for finding cumulative probabilities in a standard normal distribution. #### Description of the Table - **Columns and Rows**: - The first column (`Z`) lists z-scores from 0.0 to 3.0 in increments of 0.1. - The remaining columns provide additional precision by listing the probability values for increments of 0.01 from 0.00 to 0.09. - **Entries**: - Each entry in the table gives the probability that a standard normal variable will fall below the given z-score. - For example, to find the area under the curve to the left of z = 1.23, locate the row for `z = 1.2` and the column `0.03`. The intersecting value, 0.8907, is the area under the normal curve to the left of z = 1.23. #### How to Use the Table 1. **Locate z-score**: Identify the z-score for which you want to find the cumulative probability. For example, if you have a z-score of 1.25: - Find the row corresponding to the z-score's integer and first decimal place (`1.2`). - Find the column corresponding to the hundredths place (`0.05`). 2. **Find the Probability**: - Intersection of the row and column provides the cumulative probability up to that z-score. #### Working with Negative Z-Scores Due to the symmetry of the normal distribution curve: - For a negative z-score, simply find the positive z-score and subtract the table value from 1. - For example, to find the area to the left of z = -1.25: - Locate the value for z = 1.25 (0.8944). - Subtract it from 1: \(1 - 0.8944 = 0.1056\). ### Table Example Explained ``` Z 0.00 0.01 0.02 0.03 0.04
**Bowling Scores Probability Analysis** Recently, the bowling scores of a certain bowler were normally distributed with a mean of 202 and a standard deviation of 19. **a)** Find the probability that a score is from 185 to 210. **b)** Find the probability that a score is from 165 to 175. **c)** Find the probability that a score is greater than 200. **d)** The best score is 299. Find the percentile that corresponds to this score, and explain what that number represents. *Click the icon to view the standard normal distribution table.* --- **a)** The probability that a score is from 185 to 210 is **0.4760**. *(Round to four decimal places as needed.)* **b)** The probability that a score is from 165 to 175 is **0.0522**. *(Round to four decimal places as needed.)* **c)** The probability that a score is greater than 200 is **0.5419**. *(Round to four decimal places as needed.)* **d)** The \( \_ \)th percentile corresponds to this score, which means that 299 is \(\_ \) than \(\_ \) % of all his other scores. *(Round to five decimal places as needed.)*
Transcribed Image Text:**Bowling Scores Probability Analysis** Recently, the bowling scores of a certain bowler were normally distributed with a mean of 202 and a standard deviation of 19. **a)** Find the probability that a score is from 185 to 210. **b)** Find the probability that a score is from 165 to 175. **c)** Find the probability that a score is greater than 200. **d)** The best score is 299. Find the percentile that corresponds to this score, and explain what that number represents. *Click the icon to view the standard normal distribution table.* --- **a)** The probability that a score is from 185 to 210 is **0.4760**. *(Round to four decimal places as needed.)* **b)** The probability that a score is from 165 to 175 is **0.0522**. *(Round to four decimal places as needed.)* **c)** The probability that a score is greater than 200 is **0.5419**. *(Round to four decimal places as needed.)* **d)** The \( \_ \)th percentile corresponds to this score, which means that 299 is \(\_ \) than \(\_ \) % of all his other scores. *(Round to five decimal places as needed.)*
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