Question

the reading speed of second grade students in a large city is approximately normal, with the mean of 89 words per minute (wpm) and a standard deviation of 10 wpm

a.) what is the probability a randomly selected student in the city will read more than 94 words per minute?

b.) what is the probability that a random sample of 11 second grade students from the city results in a mean reading rate of more than 94 words per minute?

c.) what is the probabilty that a random sample od 22 second grade students from the city resulta in a mean rate of more than 94 words per minute?

The reading speed of second grade students in a large city is approximately normal, with a mean of 89 words per minute (wpm) and a standard deviation (a) What is the probability a randomly selected student in the city will read more than 94 words per minute? The probability is (Round to four decimal places as needed.) (b) What is the probability that a random sample of 11 second grade students from the city results in a mean reading rate of more than 94 words per minut The probability is (Round to four decimal places as needed.) (c) What is the probability that a random sample of 22 second grade students from the city results in a mean reading rate of more than 94 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 o decreases as n increases O B. Increasing the sample size decreases the probability because o, increases as n increases O C. Increasing the sample size increases the probability because o- decreases as n increases O D. Increasing the sample size increases the probability because o increases as n increases

Answer 1

Let X follows N(u = 89,0 =10) a) P(X>94)=P(454, 94.80) =1- P(z 50.50) =1-0.6915 = 0.3085 (Using z-table) b) X-u P(I >94)=P2 94-89 10/ =1-P(251.66 =1-0.9513 = 0.0487 (Using z-table) c) % 10 X-u 94-89 P(I>94)=P V22 =1-P(= 52.35) =1-0.9905 (Using z-table) = 0.0095

d) Increasing the sample size decreases the probability because of decreases as n increases. Answer: Option (A)