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Math Test
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Instructor's Name
Month Day, Year
Math Test
Part 1 (25 points)
Find the standard-normal curve area that lies
a) To the right of 0.65
P (z ≥ 0.65) = (1 - .7422) = .2578
b) To the left of z = -2.13
P (z ≤ -2.13) = .0166
c) Between z = -0.34 and z = 0.62
P (-0.34 ≤ z ≤ 0.62) = P (z < 0.62) – P (z < -0.34) = (.7324 – .3669) = .3655
d) A tire store finds that the thread life of its tires is normally distributed, with a mean
of 26,640 miles and standard deviation of 4000 miles. The store sold 9000 tires this
month. How many of them can be expected to last between 25,000 and 30,000 miles?
Mean = 26,640
Standard deviation (SD) = 4000
𝑧=
𝑧=
𝑧=
𝑥 − 𝑚𝑒𝑎𝑛
𝑆𝐷
25,000 − 26,640
= −0.41
4000
30,000 − 26,640
= 0.84
4000
P (-0.41 < z < 0.84) = P (z < 0.84) – P (z < -0.41) = (0.7995 – 0.3409) = 0.4586
0.4586 ×9000 = 4127.4
Approximately 4,127 of tires sold this month are expected to last between 25,000 and
30,000 miles.
Part 2 (15 points)
a) From a random sample of 36 business days, the average closing price of Apple stock
was $116.16 with a standard deviation of $10.27. Construct a 90% and 95%
confi...