A Density Curve

Question 1 Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to the point (0.7, 1). The second goes from (0.7, 1) to (0.9, 2) in the xy-plane. What percent of observations fall below 0.20?
a) 0.80
b) 1.00
c) 0.40
d) 0.10
e) 0.20
f) None of the above
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Question 2 Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to the point (0.1, 1). The second goes from (0.1, 1) to (0.7, 2) in the xy-plane. What percent of observations fall between 0.1 and 0.7?
a) 1.00
b) 0.90
c) 0.05
d) 0.10
e) 0.50
f) None of the above
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Question 3 Consider a uniform density curve defined from x = 0 to x = 7. What percent of observations fall below 4?
a) 0.25
b) 0.57
c) 0.69
d) 0.14
e) 0.40
f) None of the above
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Question 4 Consider a uniform density curve defined from x = 0 to x = 9. What percent of observations fall between 1 and 6?
a) 0.17
b) 0.68
c) 0.56
d) 0.67
e) 0.11
f) None of the above
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Question 5 Consider a spinner that, after a spin, will point to a number between zero and 1 with “uniform probability”. Determine the probability: P(¹⁄₇ ≤ X ≤ ¹⁹⁄₃₅).
a) 0.40
b) 0.54
c) 0.60
d) 1.00
e) 0.14
f) None of the above
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Question 6 The heights of students in a class are normally distributed with mean 54 inches and standard deviation 6 inches. Use the Empirical Rule to determine the interval that contains the middle 99.7% of the heights.
a) [42, 66]
b) [36, 72]
c) [48, 66]
d) [33, 75]
e) [48, 60]
f) None of the above
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Question 7 The length of time needed to complete a certain test is normally distributed with mean 77 minutes and standard deviation 11 minutes. Find the probability that it will take less than 63 minutes to complete the test.
a) 0.0508
b) 0.9492
c) 0.1016
d) 0.5000
e) 0.8984
f) None of the above
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Question 8 If X is normally distributed with a mean of 20 and a standard deviation of 2, find P(20 ≤ X ≤ 22.6).
a) 0.903
b) 0.503
c) 0.703
d) 0.403
e) 0.603
f) None of the above
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Question 9 Suppose that X is normally distributed with a mean of 60 and a standard deviation of 3. What is P(X ≥ 64.05)?
a) 0.089
b) 0.092
c) 0.091
d) 0.411
e) 0.911
f) None of the above
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Question 10 Suppose that x is normally distributed with a mean of 50 and a standard deviation of 8. What is P(x ≤ 65.60)?
a) 0.974
b) 0.474
c) 0.477
d) 0.026
e) 0.978
f) None of the above
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Question 11 Suppose that x is normally distributed with a mean of 20 and a standard deviation of 6. What is P(13.82 ≤ x ≤ 29.18)?
a) 0.351
b) 0.437
c) 0.785
d) 0.440
e) 0.348
f) None of the above
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Question 12 At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 79 and a standard deviation of 15. The scores on the calculus final are also approximately normally distributed, with a mean of 79 and a standard deviation of 12. A student scored 80 on the chemistry final and 82 on the calculus final. Relative to the students in each respective class, in which subject did the student do better?
a) There is no basis for comparison
b) The student did equally well in each course
c) Calculus
d) Chemistry
e) None of the above
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Question 13 Find a value of c so that P(Z ≤ c) = 0.53.
a) -0.08
b) 0.58
c) 0.92
d) 1.08
e) 0.08
f) None of the above