The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 17 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x = ?x = (b) Answer part (a) for a random sample of 45 individuals. (Round your answers to three decimal places.) ?x = ?x = (c) Draw a picture of the approximate sampling distribution of x when n = 45. A graph has a horizontal axis with values from approximately −3.5 to 3.5. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero. A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0.35 and 0.65 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments. A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0 and 1 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments. A graph has a horizontal axis with values from approximately 0.35 to 0.65. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0.5 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero.

The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 17 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x = ?x = (b) Answer part (a) for a random sample of 45 individuals. (Round your answers to three decimal places.) ?x = ?x = (c) Draw a picture of the approximate sampling distribution of x when n = 45. A graph has a horizontal axis with values from approximately −3.5 to 3.5. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero. A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0.35 and 0.65 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments. A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0 and 1 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments. A graph has a horizontal axis with values from approximately 0.35 to 0.65. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0.5 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Question

The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution

? = 0.5

and

? = 0.289.

(a)

Let x be the sample mean waiting time for a random sample of 17 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.)

?_x	=
?_x	=

(b)

Answer part (a) for a random sample of 45 individuals. (Round your answers to three decimal places.)

?_x	=
?_x	=

(c)

Draw a picture of the approximate sampling distribution of x when n = 45.

A graph has a horizontal axis with values from approximately −3.5 to 3.5. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero.

A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0.35 and 0.65 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments.

A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0 and 1 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments.

A graph has a horizontal axis with values from approximately 0.35 to 0.65. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0.5 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero.

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