The reading speed of second grade students in a large city is approximately norm
ID: 3220145 • Letter: T
Question
The reading speed of second grade students in a large city is approximately normal, with a mean of
89
words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (e).
(a) What is the probability a randomly selected student in the city will read more than
94
words per minute?
The probability is
. 5
.
(Round to four decimal places as needed.)
(b) What is the probability that a random sample of
10
second grade students from the city results in a mean reading rate of more than
94
words per minute?
The probability is
nothing
.
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of
20
second grade students from the city results in a mean reading rate of more than
94
words per minute?
The probability is
nothing
.
(Round to four decimal places as needed.)
(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.
A.
Increasing the sample size decreases the probability because
sigma Subscript x overbar
increases as n increases.
B.
Increasing the sample size increases the probability because
sigma Subscript x overbar
decreases as n increases.
C.
Increasing the sample size increases the probability because
sigma Subscript x overbar
increases as n increases.
D.
Increasing the sample size decreases the probability because
sigma Subscript x overbar
decreases as n increases.
(e) A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of
19
second grade students was
91.5
wpm. What might you conclude based on this result? Select the correct choice and fill in the answer box in your choice below.
(Round to four decimal places as needed.)
A.
A mean reading rate of
91.5
wpm is not unusual since the probability of obtaining a result of
91.5
wpm or more is
nothing
.
The new program is not abundantly more effective than the old program.
B.
A mean reading rate of
91.5
wpm is unusual since the probability of obtaining a result of
91.5
wpm or more is
nothing
.
The new program is abundantly more effective than the old program.
Explanation / Answer
(a) = 89, = 10, x = 94
z = (94 - 89)/10 = 0.5
P(x > 94) = P(z > 0.5) = 0.3085
(b) = 89, = 10, n = 10, x-bar = 94
z = (94 - 89)/(10/10) = 1.5811
P(x-bar > 94) = P(z > 1.5811) = 0.0569
(c) = 89, = 10, n = 20, x-bar = 94
z = (94 - 89)/(10/20) = 2.2361
P(x-bar > 94) = P(z > 2.2361) = 0.0127
(d) Increasing n increases the value of z and therefore the probability decreases
(e) A mean reading rate of 91.5 wpm is not unusual since the probability of obtaining a result of 91.5 wpm or more is 0.1379.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.