Question

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 of 10 wpm. Complete parts​ (a) through​ (f).

​(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 13 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.)

​(c) What is the probability that a random sample of 26 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.)

​(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 18 second grade students was 91.4 wpm. What might you conclude based on this​ result?

​(Type integers or decimals rounded to four decimal places as​ needed.)

A. A mean reading rate of 91.4 wpm is unusual since the probability of obtaining a result of 91.4 wpm or more is ___ This means that we would expect a mean reading rate of 91.4 or higher from a population whose mean reading rate is 89 in ____ of every 100 random samples of size n = 18 students. The new program is abundantly more effective than the old program.

B. A mean reading rate of 91.4 wpm is not unusual since the probability of obtaining a result of 91.4 wpm or more is ____ . This means that we would expect a mean reading rate of 91.4 or higher from a population whose mean reading rate is 89 in ____ of every 100 random samples of size n= 18 students. The new program is not abundantly more effective than the old program. ​

(f) There is a​ 5% chance that the mean reading speed of a random sample of 21 second grade students will exceed what​ value? There is a​ 5% chance that the mean reading speed of a random sample of ____ second grade students will exceed nothing wpm. ​

(Round to two decimal places as​ needed.)

Answer 1

B. A mean reading rate of 91.4 wpm is not unusual since the probability of obtaining a result of 91.4 wpm or more is 0.1543. This means that we would expect a mean reading rate of 91.4 or higher from a population whose mean reading rate is 89 in 15 of every 100 random samples of size n= 18 students. The new program is not abundantly more effective than the old program. ​