Suppose that the mean value of x is 22.0 and that the standard deviation is 16.1. If a random sample of
n = 100 customers
is to be selected and
x
denotes the sample mean number of checks written during a particular month, where is the sampling distribution of
x
centered?
What is the standard deviation of the sampling distribution of
x?
Sketch a rough picture of the sampling distribution.
A curve is above a horizontal axis labeled "x bar."
The horizontal axis ranges from about −5.5 to about 5.5.
The curve enters the viewing window near −5.5 just above the horizontal axis, goes up and to the right, and reaches a maximum near 0.
The curve then goes down and to the right until it leaves the viewing window at the same height it entered near 5.5.
A curve is above a horizontal axis labeled "x bar."
The horizontal axis ranges from about −3.5 to about 3.5.
The curve enters the viewing window near −3.5 just above the horizontal axis, goes up and to the right, and reaches a maximum near 0.
The curve then goes down and to the right until it leaves the viewing window at the same height it entered near 3.5.
A curve is above a horizontal axis labeled "x bar."
The horizontal axis ranges from about 16.5 to about 27.5.
The curve enters the viewing window near 16.5 just above the horizontal axis, goes up and to the right, and reaches a maximum near 22.
The curve then goes down and to the right until it leaves the viewing window at the same height it entered near 27.5.
A curve is above a horizontal axis labeled "x bar."
The horizontal axis ranges from about 18.5 to about 25.5.
The curve enters the viewing window near 18.5 just above the horizontal axis, goes up and to the right, and reaches a maximum near 2.
The curve then goes down and to the right until it leaves the viewing window at the same height it entered near 25.5.
(c)
What is the approximate probability that
x
is at most 20? (Round your answer to four decimal places.)
What is the approximate probability that
x
is at least 25? (Round your answer to four decimal places.)