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A certain swimming pool has a large population of people who swim for a distance that follows a normal distribution with a mean of 250 meters and a standard deviation of 30 meters. Randomly sample 36 swimmers. How many meters swum is the mean for the bottom 85% of all samples? Solve for h such that P (

A certain swimming pool has a large population of people who swim for a distance that follows a normal distribution with a mean of 250 meters and a standard deviation of 30 meters. Randomly sample 36 swimmers. How many meters swum is the mean for the bottom 85% of all samples? Solve for h such that P (

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A certain swimming pool has a large population of people who swim for a distance that follows a normal distribution with a mean of 250 meters and a standard deviation of 30 meters. Randomly sample 36 swimmers. How many meters swum is the mean for the bottom 85% of all samples? Solve for \( h \) such that \( P(\bar{x} < h) = 0.85 \). **Diagram:** The diagram is a normal distribution curve centered at the mean of 250 meters. The shaded area under the curve represents the portion of the distribution where the sample mean \( \bar{x} \) is less than \( h \), corresponding to the bottom 85% of the distribution. The x-axis shows the range from 230 to 270 meters, and various points are marked with their corresponding z-scores: - At 230 meters, \( z = -4 \). - At 235 meters, \( z = -3 \). - At 240 meters, \( z = -2 \). - At 245 meters, \( z = -1 \). - At 250 meters, \( z = 0 \). - At 255 meters, \( \bar{x} = h \). - At 260 meters, \( z = 2 \). - At 265 meters, \( z = 3 \). - At 270 meters, \( z = 4 \). **Calculation:** Round your answer to 2 decimal places. \( h = \_\_\_\_\_ \)
Transcribed Image Text:A certain swimming pool has a large population of people who swim for a distance that follows a normal distribution with a mean of 250 meters and a standard deviation of 30 meters. Randomly sample 36 swimmers. How many meters swum is the mean for the bottom 85% of all samples? Solve for \( h \) such that \( P(\bar{x} < h) = 0.85 \). **Diagram:** The diagram is a normal distribution curve centered at the mean of 250 meters. The shaded area under the curve represents the portion of the distribution where the sample mean \( \bar{x} \) is less than \( h \), corresponding to the bottom 85% of the distribution. The x-axis shows the range from 230 to 270 meters, and various points are marked with their corresponding z-scores: - At 230 meters, \( z = -4 \). - At 235 meters, \( z = -3 \). - At 240 meters, \( z = -2 \). - At 245 meters, \( z = -1 \). - At 250 meters, \( z = 0 \). - At 255 meters, \( \bar{x} = h \). - At 260 meters, \( z = 2 \). - At 265 meters, \( z = 3 \). - At 270 meters, \( z = 4 \). **Calculation:** Round your answer to 2 decimal places. \( h = \_\_\_\_\_ \)
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