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. 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 22 second grade students was 91.2 wpm. What might you conclude based on this​ result?

Select the correct choice below and fill in the answer boxes within your choice. ​(Type integers or decimals rounded to four decimal places as​ needed.)

A. A mean reading rate of 91.2 wpm is not unusual since the probability of obtaining a result of 91.2 wpm or more is ____. This means that we would expect a mean reading rate of 91.2 or higher from a population whose mean reading rate is 89 in _____ of every 100 random samples of size n=22 students. The new program is not abundantly more effective than the old program.

B. A mean reading rate of 91.2 wpm is unusual since the probability of obtaining a result of 91.2 wpm or more is ______. This means that we would expect a mean reading rate of 91.2 or higher from a population whose mean reading rate is 89 in _____ of every 100 random samples of size n=22 students. The new program is abundantly more effective than the old program.

Answer 1

n = sample size = 22

Let X follows  approximately​ normal, with a mean of 89 words per minute​ (wpm) and a standard deviation of 10 wpm

First we need to find P( > 91.2 ) = 1 - P ( < 91.2) ....( 1 )

The mean of sample mean is 89

and the new standard deviation of the sample mean is as

Let's use excel:

P ( < 91.2) ="=NORMDIST(91.2,89,2.132,1)" = 0.8489

Plug this in equation ( 1 ).

P( > 91.2 ) = 1 - 0.8489 = 0.1511

Since 0.1511 > 0.05 , it is usual, so correct option is A.

A. A mean reading rate of 91.2 wpm is not unusual since the probability of obtaining a result of 91.2 wpm or more is 0.1511. This means that we would expect a mean reading rate of 91.2 or higher from a population whose mean reading rate is 89 in 15 of every 100 random samples of size n=22 students. The new program is not abundantly more effective than the old program.