A set of final examination grades in an introductory statistics course is normally​ distributed, with a mean of 77 and a standard deviation of 8. Complete parts​ (a) through​ (d).       Question content area bottom Part 1 a. What is the probability that a student scored below 86 on this​ exam?   The probability that a student scored below 86 is enter your response here. ​(Round to four decimal places as​ needed.)   b. What is the probability that a student scored between 69 and 100​?   The probability that a student scored between 69 and 100 is enter your response here. ​(Round to four decimal places as​ needed.)   c. The probability is 15​% that a student taking the test scores higher than what​ grade?   The probability is 15​% that a student taking the test scores higher than enter your response here. ​(Round to the nearest integer as​ needed.)

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A set of final examination grades in an introductory statistics course is normally​ distributed, with a mean of
77
and a standard deviation of
8.
Complete parts​ (a) through​ (d).
 
 
 

Question content area bottom

Part 1
a.
What is the probability that a student scored below
86
on this​ exam?
 
The probability that a student scored below
86
is
enter your response here.
​(Round to four decimal places as​ needed.)
 
b.
What is the probability that a student scored between
69
and
100​?
 
The probability that a student scored between
69
and
100
is
enter your response here.
​(Round to four decimal places as​ needed.)
 
c.
The probability is
15​%
that a student taking the test scores higher than what​ grade?
 
The probability is
15​%
that a student taking the test scores higher than
enter your response here.
​(Round to the nearest integer as​ needed.)
 
d.
If the professor grades on a curve​ (for example, the professor could give​ A's to the top​ 10% of the​ class, regardless of the​ score), is a student better off with a grade of
85
on this exam or a grade of
74
on a different​ exam, where the mean is
66
and the standard deviation is
4​?
Show your answer statistically and explain.
 
A student is
 
better off
worse off
with a grade of
85
on this exam because the Z value for the grade of
85
is
enter your response here
and the Z value for the grade of
74
is
enter your response here. 
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