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 92 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f) (a) What is the probability a randomly selected student will read more than 97 words per minute? The probability is (Round to four decimal places as needed.) (b) What is the probability that a random sample of 14 second grade students results in a mean reading rate of more than 97 words per minute? The probability is (Round to four decimal places as needed.) (c) What is the probability that a random sample of 28 second grade students results in a mean reading rate of more than 97 words per minute? The probability is (Round to four decimal places as needed.) (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. O A. Increasing the sample size decreases the probability because decreases as n increases. O B. Increasing the sample size decreases the probability because increases as n increases. Click to select your answer(s)

Explanation / Answer

mean is 92 and s is 10

a) z is given as (x-mean)/s thus P(x>97)=P(z>(97-92)/10)=P(z>0.5) or 1-P(z<0.5), from normal distribution table we get 1-0.6915=0.3085

b) for 14 sample size the z value is (x-mean)/(s/sqrt(N)) thus P(z>(97-92)/(10/sqrt(14)))=P(z>1.87) or 1-P(z<1.87)

from normal distribution table we get 1-0.9693=0.0307

c) for 28 sample size the , P(z>(97-92)/(10/sqrt(28)))=P(z>2.65) or 1-P(z<2.65)

from normal distribution table we get 1-0.9960=0.004

thus A

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