교과서 질문
Which is larger, the area under the t-distribution with 10 degrees of freedom to the right of t = 2.30 or the area under the standard normal distribution to the right of z = 2.32? Why?
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
객관식
In the (standard normal distribution), what happens to the graph of the normal curve as the mean increases while the standard deviation remains constant?
A
The curve shifts upward along the vertical axis.
B
The curve becomes taller and narrower.
C
The curve becomes shorter and wider.
D
The entire curve shifts to the right along the horizontal axis without changing its shape.
검증된 단계별 안내1
Recall that the standard normal distribution is a normal distribution with mean \( \mu = 0 \) and standard deviation \( \sigma = 1 \).
Understand that the mean \( \mu \) determines the center or location of the normal curve along the horizontal axis (x-axis).
Recognize that changing the mean \( \mu \) shifts the entire curve left or right without altering its shape, because the standard deviation \( \sigma \) remains constant.
Note that the standard deviation \( \sigma \) controls the spread or width of the curve; since it remains constant, the height and width of the curve do not change.
Therefore, increasing the mean \( \mu \) moves the curve to the right along the horizontal axis, but the curve's shape (height and width) stays the same.
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