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1 | | Find P(-0.5 < Z < 0.5). |
| | A) | 0.3830 |
| | B) | 0.1915 |
| | C) | 0.6515 |
| | D) | 0.3085 |
| | E) | none of the above |
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2 | | Find the probability that a standard normal random variable has a value greater than -1.56. |
| | A) | 0.0332 |
| | B) | 0.0594 |
| | C) | 0.9406 |
| | D) | 0.9668 |
| | E) | none of the above |
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3 | | Let X be a normally distributed random variable with mean 100 and standard deviation 20. Find two values, a and b, symmetric about the mean, such that the probability of the random variable being between them is 0.99. |
| | A) | 90.5, 105.9 |
| | B) | 80.2, 119.8 |
| | C) | 22, 78 |
| | D) | 48.5, 151.5 |
| | E) | 90.1, 109.9 |
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4 | | A spark plug manufacturer believes that his plug lasts an average of 30,000 miles, with a standard deviation of 2,500 miles. What is the probability that a given spark plug of this type will last 37,500 miles before replacement? |
| | A) | 0.0228 |
| | B) | 0.0114 |
| | C) | 0.0013 |
| | D) | 0.0714 |
| | E) | 0.0833 |
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5 | | The contents of a particular bottle of shampoo marked as 150 ml are found to be 153 ml at an average, with a standard deviation of 2.5 ml. What proportion of shampoo bottles contain less than the marked quantity? Assume a normal distribution. |
| | A) | 0.2192 |
| | B) | 0.1151 |
| | C) | 0.4452 |
| | D) | 0.0548 |
| | E) | none of the above |
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6 | | A grocery store has a mean accounts receivable of $264, with a standard deviation of $55. The accounts receivable are normally distributed. What proportion of all accounts will be greater than $275? |
| | A) | 0.2 |
| | B) | 0.1 |
| | C) | 0.4207 |
| | D) | 0.0793 |
| | E) | 0.0228 |
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7 | | A grocery store has a mean accounts receivable of $264, with a standard deviation of $55. The accounts receivable are approximately normally distributed. Find the value such that 45% of all the accounts exceed this value. That is, find x such that: P(X > x) = 0.45. |
| | A) | $257.13 |
| | B) | $354.48 |
| | C) | $270.91 |
| | D) | $309.00 |
| | E) | none of the above |
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8 | | The IQs of the employees of a company are normally distributed, with a mean of 127 and a standard deviation of 11. What is the probability that the IQ of an employee selected at random will be between 120 and 130? |
| | A) | 0.2389 |
| | B) | 0.3453 |
| | C) | 0.1064 |
| | D) | 0.1325 |
| | E) | 0.4638 |
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9 | | The GMAT scores of students in a college are normally distributed with a mean of 520 and a standard deviation of 41. What proportion of students have a score higher than 600? |
| | A) | 0.9744 |
| | B) | 0.2372 |
| | C) | 0.4774 |
| | D) | 0.0255 |
| | E) | none of the above |
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10 | | A normal random variable has a distribution that is: |
| | A) | always symmetric |
| | B) | never symmetric |
| | C) | sometimes symmetric |
| | D) | symmetric if the mean is positive |
| | E) | symmetric if the variance is negative |
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11 | | What is the probability that a normal random variable with mean 15 and standard deviation 5 will have a value of exactly 25? |
| | A) | 0.0228 |
| | B) | 0.0456 |
| | C) | 0.9772 |
| | D) | 0 |
| | E) | 1 |
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12 | | If X is a normal random variable with mean 15 and standard deviation 10, then the probability that X will have a negative value is: |
| | A) | 0.0668 |
| | B) | 0.432 |
| | C) | 0.9332 |
| | D) | 0.8664 |
| | E) | none of the above |
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