The reading speed of a second grade students in a large city is approximately normal with a mean of 92 words per minute and a standard deviation of 10 wpm. What is the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm?

Question

Mathematics

Mauricio Russo

2 April, 16:21

The reading speed of a second grade students in a large city is approximately normal with a mean of 92 words per minute and a standard deviation of 10 wpm. What is the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm?

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Ivan Pacheco · Answer 1

Let X be a random variable representing the mean reading speed of a sample of second grade students in the city.

P (X > 96) = 1 - P (X ≤ 96) = 1 - P (X ≤ (96 - 92) / (10/sqrt (28)) = 1 - P (X ≤ 2.117) = 1 - 0.98285 = 0.01715

Required probablility = 0.01715