The reading speed of second grade students is approximately

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.

1. What is the probability a randomly selected student will read more thatn 96 words per minute? ( round to four decimal olaces as needed)

2. What is the probability that a random sample of 11 second grade students results in a mean reading rate of more that 96 words per minute?(round to four decimal places as needed

3. What is the probability that a random sample of 22 second grade students results in a mean reading rate of more than 96 words per minute? ( round to four decimal olaces as needed)

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

a. increasing the sample size decreases the probability because Ox increasing as n increase.

b. increasing the sample size increases the probability because Ox increasing as n increase.

c. increasing the sample size increases the probability because Ox decreasing as n increase.

d. increasing the sample size decreases the probability because Ox decreasing as n increase.

5. 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 second grade students was 94.4 wpm. What might you conclude based on this result? ( round to four decimal places as needed)

a. A mean reading rate of 94.4 wpm is unusual since the probability of obatining a result of 94.4 wpm or more is __. The new program is abundantly more effective than the old program.

b. A mean reading rate of 94.4 wpm is unusual since the probability of obatining a result of 94.4 wpm or more is __. The new program is not abundantly more effective than the old program.

6. There is a 5% chance that the mean reading speed of a random sample of 19second grade students will exceed what value?

There is a 5% chance of the mean value exceeding __ wpm. ( ROUND TO ONE DECIMAL PLACE AS NEEDED)

Solution

Answer to question# 1)

M = 92

s = 10

P(x > 96) = 1 - P( x< 96)

P(X < 96) = P(z < (96-92)/10) = P(z < 0.4) = 0.6554

P(x>96) = 1 - 0.6554

P(x>96) = 0.3446