The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of

225

is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning.

	(a)	(b)	(c)
05000.04Time(insec.)Rel.frequency P(x) x =16.9 =12.3 A graph has a coordinate system with a horizontal x-axis labeled Time (in seconds) from 0 to 50 in increments of 10 and a vertical P(x)-axis labeled Relative frequency from 0 to 0.04 in increments of 0.005. A curve labeled mu = 16.9 and sigma = 12.3 falls from left to right at an increasing rate from the point (0, 0.036) to the point (42, 0). A dashed vertical line segment extends from the horizontal axis to the curve at 16.9. All coordinates are approximate.	-404000.04Time(insec.)Rel.frequency Px x x=1.1 x=12.3 A graph labeled (a) has a coordinate system with a horizontal x overbar-axis labeled Time (in seconds) from negative 40 to 40 in increments of 10 and a vertical Upper P left parenthesis x overbar right parenthesis-axis labeled Relative frequency from 0 to 0.04 in increments of 0.005. A bell-shaped curve labeled mu Subscript x overbar = 1.1 and sigma Subscript x overbar = 12.3 is over the horizontal axis and is centered on 1.1. A dashed vertical line segment extends from the horizontal axis to the curve at 1.1.	-205000.04Time(insec.)Rel.frequency Px x x=16.9 x=12.3 A graph labeled (b) has a coordinate system with a horizontal x overbar-axis labeled Time (in seconds) from negative 20 to 50 in increments of 10 and a vertical Upper P left parenthesis x overbar right parenthesis-axis labeled Relative frequency from 0 to 0.04 in increments of 0.005. A bell-shaped curve labeled mu Subscript x overbar = 16.9 and sigma Subscript x overbar = 12.3 is over the horizontal axis and is centered on 16.9. A dashed vertical line segment extends from the horizontal axis to the curve at 16.9.	05000.55Time(insec.)Rel.frequency Px x x=16.9 x=0.82 A graph labeled (c) has a coordinate system with a horizontal x overbar-axis labeled Time (in seconds) from 0 to 50 in increments of 10 and a vertical Upper P left parenthesis x overbar right parenthesis-axis labeled Relative frequency from 0 to 0.550 in increments of 0.05. A bell-shaped curve labeled mu Subscript x overbar = 16.9 and sigma Subscript x overbar = 0.82 is over the horizontal axis and is centered on 16.9. A dashed vertical line segment extends from the horizontal axis to the curve at 16.9.

Question content area bottom

Part 1

Graph

(a)

(b)

(c)

most closely resembles the sampling distribution of the sample means, because

x=enter your response here,

x=enter your response here,

and the graph

approximates a normal curve

is the same shape as the graph for the original distribution

.