An education researcher has been studying test anxiety using a particular measure, which she administers to students prior to midterm exams. On this measure, she has found that the distribution follows a normal curve. The measure has a mean of 13
and a standard deviation of 4.
Using the accompanying normal curve table, what percentage of students have scores (a) above 22,
(b) above
20,
(c) above
19,
(d) below
19,
and
(e) below
4?
Solution :
Given that ,
mean = = 13
standard deviation = = 4
(a)
P(x > 22) = 1 - P(x < 22)
= 1 - P[(x - ) / < (22 - 13) / 4]
= 1 - P(z < 2.25)
= 1 - 0.9878
= 0.0122
percentage = 1.22%
(b)
P(x > 20) = 1 - P(x < 20)
= 1 - P[(x - ) / < (20 - 13) / 4]
= 1 - P(z < 1.75)
= 1 - 0.9599
= 0.0401
percentage = 4.01%
(c)
P(x > 19) = 1 - P(x < 19)
= 1 - P[(x - ) / < (19 - 13) / 4]
= 1 - P(z < 1.5)
= 1 - 0.9332
= 0.0668
percentage = 6.68%
(d)
P(x < 19) = P[(x - ) / < (19 - 13) / 4]
= P(z < 1.5)
= 0.9332
Percentage = 93.32%
(e)
P(x < 4) = P[(x - ) / < (4 - 13) / 4]
= P(z < -2.25)
= 0.0122
Percentage = 1.22%
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