The reading speed of second grade students is approximately normal, with a mean

Question

The reading speed of second grade students is approximately normal, with a mean of 88 words per minute (wpm) and a standard deviation of 12 wpm.

a) A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of 20 second grade students was 92.8 wpm. What might you conclude based on this result?

b) There is a 5% chance that the mean reading speed of a random sample of 20 second grade students will exceed what value?

Explanation / Answer

a)

z-value corresponding to 92.8 = (92.8 - 88)/(12/sqrt(20)) = 1.7888

p-value corresponding to 1.7888 is 1 - 0.96318 = 0.03682

So, there is 3.682 % chance that new program has improved mean reading speed of the students.

b)

for p-value of 5%, z- value = 1.645

Corresponding mean value = 88 + 12*1.645/sqrt(20) = 92.414 wpm

There is 5 % chance that the mean reading speed of random sample of 20 second grade students will exceed 92.414 wpm.

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