Question

The reading speed of second grade students in a large city is approximately​ normal, with a mean of

88

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

92

words per​ minute?The probability is

​(Round to four decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.If 100 different students were chosen from this​ population, we would expect

nothing

to read exactly

92

words per minute.

B.If 100 different students were chosen from this​ population, we would expect

to read more than

9292

words per minute.

C.If 100 different students were chosen from this​ population, we would expect

nothing

to read less than

92

words per minute.​(b) What is the probability that a random sample of

12

second grade students from the city results in a mean reading rate of more than

92

words per​ minute?The probability is

nothing.

​(Round to four decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.If 100 independent samples of

nequals=12

students were chosen from this​ population, we would expect

nothing

​sample(s) to have a sample mean reading rate of less than

92

words per minute.

B.If 100 independent samples of

nequals=12

students were chosen from this​ population, we would expect

nothing

​sample(s) to have a sample mean reading rate of more than

92

words per minute.

C.If 100 independent samples of

nequals=12

students were chosen from this​ population, we would expect

nothing

​sample(s) to have a sample mean reading rate of exactly

92

words per minute.​(c) What is the probability that a random sample of

24

second grade students from the city results in a mean reading rate of more than

92

words per​ minute?The probability is

nothing.

​(Round to four decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.If 100 independent samples of

nequals=24

students were chosen from this​ population, we would expect

nothing

​sample(s) to have a sample mean reading rate of less than

92

words per minute.

B.If 100 independent samples of

nequals=24

students were chosen from this​ population, we would expect

nothing

​sample(s) to have a sample mean reading rate of more than

92

words per minute.

C.If 100 independent samples of

nequals=24

students were chosen from this​ population, we would expect

nothing

​sample(s) to have a sample mean reading rate of exactly

92

words per minute.

​(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result.

A.Increasing the sample size increases the probability because

sigma Subscript x overbarσx

decreases as n increases.

B.Increasing the sample size increases the probability because

sigma Subscript x overbarσx

increases as n increases.

C.Increasing the sample size decreases the probability because

sigma Subscript x overbarσx

increases as n increases.

D.Increasing the sample size decreases the probability because

sigma Subscript x overbarσx

decreases as n increases.​(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

19

second grade students was

90.5

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

90.5

wpm is unusual since the probability of obtaining a result of

90.5

wpm or more is

nothing.

This means that we would expect a mean reading rate of

90.5

or higher from a population whose mean reading rate is

88

in

nothing

of every 100 random samples of size

nequals=19

students. The new program is abundantly more effective than the old program.

B.A mean reading rate of

90.5

wpm is not unusual since the probability of obtaining a result of

90.5

wpm or more is

nothing.

This means that we would expect a mean reading rate of

90.5

or higher from a population whose mean reading rate is

88

in

nothing

of every 100 random samples of size

nequals=19

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

23

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

23

second grade students will exceed

nothing

wpm. ​(Round to two decimal places as​ needed.

Answer 1