(Use Excel) A professor at a local community college noted that the grades of hi
ID: 3314582 • Letter: #
Question
(Use Excel) A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's.
a. What is the minimum score needed to make an A?
b. What is the maximum score among those who received an F?
c. If there were 5 students who did not pass the course, how many students took the course?
Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 74
standard Deviation ( sd )= 10
a.
UPPER/TOP
P ( Z > x ) = 0.063
Value of z to the cumulative probability of 0.063 from normal table is 1.530068
P( x-u / (s.d) > x - 74/10) = 0.063
That is, ( x - 74/10) = 1.530068
--> x = 1.530068 * 10+74 = 89.300676
it is approximately 89
b.
P ( Z < x ) = 0.025
Value of z to the cumulative probability of 0.025 from normal table is -1.959964
P( x-u/s.d < x - 74/10 ) = 0.025
That is, ( x - 74/10 ) = -1.959964
--> x = -1.959964 * 10 + 74 = 54.40036
maximum score among those who received an F is 54.40
c.
it is said that 2.5 percent of his students failed the course and received F's
i.e 2.5% of the students is = 5
the total no.of attend is = 100 * 5 / 2.5 = 200
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