SOLUTION: the number of hours a week students devotes to study is normally distributed,with a mean of 30 hours and a standard deviation of 8 hours. a. what percent of student will study les

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Question 742883: the number of hours a week students devotes to study is normally distributed,with a mean of 30 hours and a standard deviation of 8 hours.
a. what percent of student will study less than 20 hours?
b.what percent of students will study more than 35 hours?
c. out of a class of 200 students, how many will study between 25 and 35 hours?
Found 2 solutions by reviewermath, stanbon:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
a. P(X < 20) = P%28Z+%3C+%2820+-+30%29%2F8%29
= P(Z < -1.25)
= 10.56%
b. P(X > 35) = P%28Z+%3E+%2835+-+30%29%2F8%29
= P(Z > 0.625)
= 26.60%
c. P(25 < X < 35) = P%28%2825-30%29%2F8+%3C+X+%3C+%2835-30%29%2F8%29
= P(-0.625 < Z < 0.625)
= 1 - 2(0.2660)
= 46.8%
Answer: 46.8% of 200 = 93.6 ≈ highlight%2894%29 students

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the number of hours a week students devotes to study is normally distributed,with a mean of 30 hours and a standard deviation of 8 hours.
a. what percent of student will study less than 20 hours?
z(20) = (20-30)/8 = -10/8 = -5/4
P(x < 20) = P(z < -5/4) = normalcdf(-100,-5/4) = 0.1056
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Use the same procedure on problems "b" and "c".
Cheers,
Stan H.
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b.what percent of students will study more than 35 hours?
c. out of a class of 200 students, how many will study between 25 and 35 hours?