Chapter 8 Quiz

1.  Suppose  Diane and  Jack are each attempting to use a simulation to describe the sampling distribution from a population that is skewed  with mean  70 and standard deviation 15.  Diane obtains 1000 random samples of size n = 4 from the​ population, finds the mean of the​ means, and determines the standard deviation of the means.  Jack does the same​ simulation, but obtains 1000 random samples of size n = 40 from the population. Complete parts​ (a) through​ (c) below.

​(a) Describe the shape you expect for ​’s distribution of sample means. Describe the shape you expect for ​’s distribution of sample means. Choose the correct answer below.

1. Diane​’s distribution is expected to be skewed ​, but not as much as the original distribution. Jack​’s distribution is expected to be approximately normal.
2. Diane​’s distribution and ​’s distribution are expected to be approximately normal.​ However, ​Diane’s will have a greater standard deviation.
3. Diane​’s distribution is expected to be skewed ​, but not as much as the original distribution. Jack​’s distribution is expected to be approximately normal.
4. Jack​’s distribution is expected to be skewed ​, but more than the original distribution. ​Diane’s distribution is expected to be approximately normal.

(b) What do you expect the mean of ​’s distribution to​ be? What do you expect the mean of ​’s distribution to​ be?
​Diane’s distribution is expected to have a mean of ___ . ​Jack’s distribution is expected to have a mean of  ___.

​(c) What do you expect the standard deviation of ​’s distribution to​ be? What do you expect the standard deviation of ​’s distribution to​ be?
​Diane’s distribution is expected to have a standard deviation of ____.  Jack​’s distribution is expected to have a standard deviation of _____ ​(Round to two decimal places as​ needed.)

2. 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  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.

1. If 100 different students were chosen from this​ population, we would expect ____ to read less than  words per minute.
2. If 100 different students were chosen from this​ population, we would expect ____ to read more than  93 words per minute.
3. If 100 different students were chosen from this​ population, we would expect ______ to read exactly 93 words per minute.

(b) What is the probability that a random sample of  second grade students from the city results in a mean reading rate of more than  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.

1. If 100 independent samples of n = 14 students were chosen from this​ population, we would expect ___ ​sample(s) to have a sample mean reading rate of more than 93 words per minute.
2. If 100 independent samples of n = 14 students were chosen from this​ population, we would expect ___ ​sample(s) to have a sample mean reading rate of less than 93  words per minute.
3. If 100 independent samples of n = 14 students were chosen from this​ population, we would expect ____ ​sample(s) to have a sample mean reading rate of exactly 93 words per minute.

(c) What is the probability that a random sample of  second grade students from the city results in a mean reading rate of more than  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.

1. If 100 independent samples of n = 28 students were chosen from this​ population, we would expect 2 ​sample(s) to have a sample mean reading rate of more than 93  words per minute.
2. If 100 independent samples of n = 28 students were chosen from this​ population, we would expect ___ ​sample(s) to have a sample mean reading rate of less than  words per minute.
3. If 100 independent samples of n = 28 students were chosen from this​ population, we would expect ____ ​sample(s) to have a sample mean reading rate of exactly  words per minute.