Question

A teacher wants to test all of the 10th-grade students at his school to gauge their basic mathematical understanding, but the photocopier breaks after making only six copies of the test. With no other choice, he chooses six students at random to take the test. Their results, recorded as a score out of 65 , have a sample mean of 41.1 . The standard deviation of the marks of this test is known to be 11.3. a. Find the standard error associated with the mean test score. b. Assuming the scores themselves are normally distributed, evaluate the probability that the mean score lies between 45 and 55 if the teacher took another sample of the same size. c. A student who gets less than half the questions correct receives a failing grade (F). Find the probability that the average score is an F based on another sample of the same size.

          A teacher wants to test all of the 10th-grade students at his school to gauge their basic mathematical understanding, but the photocopier breaks after making only six copies of the test. With no other choice, he chooses six students at random to take the test. Their results, recorded as a score out of 65 , have a sample mean of 41.1 . The standard deviation of the marks of this test is known to be 11.3.
a. Find the standard error associated with the mean test score.
b. Assuming the scores themselves are normally distributed, evaluate the probability that the mean score lies between 45 and 55 if the teacher took another sample of the same size.
c. A student who gets less than half the questions correct receives a failing grade (F). Find the probability that the average score is an F based on another sample of the same size.

A teacher wants to test all of the 10th-grade students at his school to gauge their basic mathematical understanding, but the photocopier breaks after making only six copies of the test. With no other choice, he chooses six students at random to take the test. Their results, recorded as a score out of 65 , have a sample mean of 41.1 . The standard deviation of the marks of this test is known to be 11.3.
a. Find the standard error associated with the mean test score.
b. Assuming the scores themselves are normally distributed, evaluate the probability that the mean score lies between 45 and 55 if the teacher took another sample of the same size.
c. A student who gets less than half the questions correct receives a failing grade (F). Find the probability that the average score is an F based on another sample of the same size.

Added by Stephen C.

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