The reading speed of second grade students in a large city is approximately norm

Question

The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).

(b) What is the probability that a random sample of 10second grade students from the city results in a mean reading rate of more than 95 words per minute?

(c) What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 95 words per minute?

(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.

(e) 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 19 econd grade students was 92.1 wpm. What might you conclude based on this result? Select the correct choice below and fill in the answer boxes within your choice.

(f) There is a 5% chance that the mean reading speed of a random sample of 24 second grade students will exceed what value?

Explanation / Answer

b)

P(z>1.58) = 1 - p(z<1.58)

= 1 - 0.9429

= 0.0571

c)

P(z>2.24) = 1 - p(z<2.24)

= 1 - .9875

= 0.0125

d) Increase the sample sizes reduces the probability.

e)

  

Given, mu       = 90 X           = 95 n          = 10 Standard Deviation (SD)= 10 Standard Error (S.E) = 3.162278 Z    = ( X - mu) / SE Z    = 1.58

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