Suppose that the test score of a student taking the final of a probability course is a random variable with mean 85. (a) Give an upper bound for the probability that a student's test score will exceed 95. P{score > 95}<≤ 585 85 95 (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 23. What can you say about the probability that a student will score between 75 and 95 (do not use the central limit theorem)? 23 P{75 score 95} (>= = 1 102 (c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 2 of 85 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? n =
Suppose that the test score of a student taking the final of a probability course is a random variable with mean 85. (a) Give an upper bound for the probability that a student's test score will exceed 95. P{score > 95}<≤ 585 85 95 (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 23. What can you say about the probability that a student will score between 75 and 95 (do not use the central limit theorem)? 23 P{75 score 95} (>= = 1 102 (c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 2 of 85 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? n =
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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Part C and D only
Transcribed Image Text:Suppose that the test score of a student taking the final of a probability course is a random variable with mean 85.
(a) Give an upper bound for the probability that a student's test score will exceed 95.
P{score > 95}<≤
585
85
95
(b) Suppose that we know, in addition, that the variance of students' test scores on the final is 23. What can you say about the probability that a student will
score between 75 and 95 (do not use the central limit theorem)?
23
P{75 score 95} (>= =
1
102
(c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 2 of 85 (do not use the
central limit theorem)?
n =
(d) If you use the central limit theorem in (c), what is your estimate for the number of students needed?
n =
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