Questions 24-27 are related to the following A large group of students took a st
ID: 3070784 • Letter: Q
Question
Questions 24-27 are related to the following A large group of students took a statistics test. The mean score, from the scale of 100, was 70 with a standard deviation of 8.5. The test scores have a bell-shaped distribution. 24 Students who scored less than 55 failed the test. What fraction of students failed the test? a 0.0392 b 0.0495 c 0.0559 d 0.0643 25 If the minimum score for the letter grade B is 76, what fraction of students received a grade of B or higher. a 0.2877 b 0.2776 c 0.2578 d 0.2389 26 If the range of scores for a C is 65-75, what fraction of students received a C? a 0.5034 b 0.4972 c 0.4844 d 0.4448 27 What should the minimum score be set at so that a grade of A is given to the top 5% of test scores? (Round your answer to the nearest integer.) a 84 b 86 c 87 d 90 Questions 24-27 are related to the following A large group of students took a statistics test. The mean score, from the scale of 100, was 70 with a standard deviation of 8.5. The test scores have a bell-shaped distribution. 24 Students who scored less than 55 failed the test. What fraction of students failed the test? a 0.0392 b 0.0495 c 0.0559 d 0.0643 25 If the minimum score for the letter grade B is 76, what fraction of students received a grade of B or higher. a 0.2877 b 0.2776 c 0.2578 d 0.2389 26 If the range of scores for a C is 65-75, what fraction of students received a C? a 0.5034 b 0.4972 c 0.4844 d 0.4448 27 What should the minimum score be set at so that a grade of A is given to the top 5% of test scores? (Round your answer to the nearest integer.) a 84 b 86 c 87 d 90Explanation / Answer
24. P(X < 55)
= P(z < (55 - 70)/8.5)
= P(z < -1.76)
= 0.0392
Option A is correct.
Similarly,
25. P(76 or higher)
= P(X > 76)
= P(z > 0.71)
= 0.2389
Option D is correct.
26. P(65 < X < 75)
= P(-0.59 < z < 0.59)
= 0.4448
Option D is correct.
27. Minimum score = 70 + 1.645*8.5 = 84
Option A is correct.
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