Question

Students in a chemistry class convince their teacher to use the following "group grading" scenario. Students will all take the exam on their own; however, the grade they receive will be the mean of their test score with 4 other randomly selected classmates. Assume that the test scores for this particular exam are normally distributed with a mean of 74 and a standard deviation of 12 points. You need an 80 or better on this exam. What is the probability that your individual test score is above 80?

Answer #1

Solution :

Given that ,

mean = = 74

standard deviation = = 12

n = 4

= 74

= / n = 12/ 4 = 6

P( > 80) = 1 - P( < 80)

= 1 - P[( - ) / < (80-74) / 6]

= 1 - P(z < 1)

Using z table

= 1 - 0.8413

= 0.1587

probability= 0.1587

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