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Quiz 5

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 0.40?

a) 0.30

b) 0.20

c) 1.00

d) 0.40

e) 0.60

f) None of the above

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 Question 3 Consider a uniform density curve defined from x = 0 to x = 9. What percent of observations fall below 7?

a) 0.70

b) 0.11

c) 0.90



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d) 0.78

e) 0.14

f) None of the above Question 4 Consider a uniform density curve defined from x = 0 to x = 6. What percent of observations fall between 1 and 4?

a) 0.50 b) 0.17 c) 0.67 d) 0.25 e) 0.62 f) None of the above 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(1/4 X 15/28).

a) 0.29 b) 1.00 c) 0.54 d) 0.25 e) 0.71 f) None of the above Question 6 The heights of students in a class are normally distributed with mean 68 inches and standard deviation 5 inches. Use the Empirical Rule to determine the interval that contains the middle 95% of the heights.

a) [55, 81] b) [58, 78]



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c) [53, 73]

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d) [53, 83]

e) [63, 73]

f) None of the above

Question 7

The length of time needed to complete a certain test is normally distributed with mean 31 minutes and standard deviation 6 minutes. Find the probability that it will take less than 40 minutes to complete the test.

a) 0.5334

b) 0.5000

c) 0.0668

d) 0.9332

e) 0.4666

f) None of the above Question 8 If X is normally distributed with a mean of 20 and a standard deviation of 4, find P(20 X 24).

a) 0.641

b) 0.341

c) 0.841

d) 0.441

e) 0.541

f) None of the above

Question 9

Suppose that X is normally distributed with a mean of 40 and a standard deviation of 15. What is P(X 52.45)?

a) 0.203

b) 0.597



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c) 0.206

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d) 0.297

e) 0.207

f) None of the above

Question 10

Suppose that x is normally distributed with a mean of 50 and a standard deviation of 10. What is P(x 74.50)?

a) 0.496

b) 0.493

c) 0.007

d) 0.993

e) 0.995

f) None of the above

Question 11

Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3. What is P(27.42 x 34.08)?

a) 0.718

b) 0.413

c) 0.309

d) 0.305

e) 0.415

f) None of the above

Question 12

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 76 and a standard deviation of 14. The scores on the calculus final are also approximately normally distributed, with a mean of 74 and a standard deviation of 15. A student scored 79 on the chemistry final and 81 on the calculus final. Relative to the students in each respective class, in which subject did the student do better?



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a) Chemistry b) Calculus c) The student did equally well in each course d) There is no basis for comparison e) None of the above Question 13 Find a value of c so that P(Z c) = 0.48. a) 0.05 b) 0.95 c) 0.45 d) -0.05 e) 1.05 f) None of the above

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Quiz 6

Question 1 Suppose that x is normally distributed with a mean of 20 and a standard deviation of 15. What is P(-7.45 x 54.95)? a) 0.956 b) 0.490 c) 0.468 d) 0.495 e) 0.466 f) None of the above Question 2 Find a value of c so that P(Z c) = 0.71. a) -1.11 b) 0.75 c) -0.55 d) 0.55 e) 1.55 f) None of the above Question 3 Suppose that x is normally distributed with a mean of 50 and a standard deviation of 15. What is P(34.55 x 72.95)? a) 0.348 b) 0.785 c) 0.442



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d) 0.353

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e) 0.437

f) None of the above

Question 4

The length of time needed to complete a certain test is normally distributed with mean 31 minutes and standard deviation 6 minutes. Find the probability that it will take between 29 and 35 minutes to complete the test.

a) 0.3694

b) 0.5000

c) 0.6219

d) 0.3781

e) 0.1890

f) None of the above

Question 5

The length of time needed to complete a certain test is normally distributed with mean 35 minutes and standard deviation 15 minutes. Find the probability that it will take more than 40 minutes to complete the test.

a) 0.3694

b) 0.6306

c) 0.5000

d) 0.1847

e) 0.8153

f) None of the above Question 6 Which of the following statements is not true?

a) The expected value of the sample mean, X, is always the same as the expected value of X, the distribution of the population from which the sample was taken.



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b) The standard deviation of the sampling distribution X of sample mean = /n where is the standard deviation of X.

c) The larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean.

d) The sampling distribution of the sample mean, X, is always reasonably like the distribution of X, the distribution from which the sample is taken.

e) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric for n > 30 or n = 30.

f) None of the above

Question 7

Suppose a random sample of 60 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x.

a) [25, 1.825]

b) [25, 1.925]

c) [60, 2.325]

d) [25, 2.225]

e) [25, 2.325]

f) None of the above

Question 8

A random sample of 400 24-ounce cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 24 ounces and a standard deviation of 0.24 ounce. What is the probability that the mean contents of the 400 sample cans is less than 23.988 ounces?

a) 0.199

b) 0.169

c) 0.209

d) 0.159

e) 0.179

f) None of the above



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