Question 1

A fair die is rolled. If the top face is a 5 or 6, you win $1; otherwise you win nothing. Let  be the amount you win in one play of the game and let  be the average amount you win in two plays of the game. Find the sampling distribution of  .

Accepted Answer

The answer of A fair die is rolled. If the...

Question 2

Lab Mice Experiments Narrative
In a learning experiment, untrained mice are placed in a maze and the time required for each mouse to exit the maze is recorded. The average time for untrained mice to exit the maze is $\mu$ = 50 seconds and the standard deviation of their times is $\sigma$ = 16 seconds. Suppose that a sample of 64 randomly selected untrained mice are placed in the maze and the time necessary to exit the maze is recorded for each.
-Refer to Lab Mice Experiments Narrative. What is the probability that the sample mean differs from the population mean by more than 3?

Accepted Answer

The answer of Lab Mice Experiments Narrative
In a learning experiment,...

Question 3

Baggage Weights Narrative
The weight of baggage checked by airline passengers is a random variable with a mean of 25 kg and a standard deviation of 12 kg. The total baggage limit for 100 randomly selected passengers is 2740 kg.
-A population consists of four numbers, 0, 1, 2, and 4. Suppose we randomly select two of those four numbers without replacement and compute the sample mean,  , of the two numbers selected. Find the sampling distribution of  .

Accepted Answer

The answer of Baggage Weights Narrative
The weight of baggage checked...

Question 4

Examination Times Narrative
The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed.
-Refer to Examination Times Narrative. Completely describe the sampling distribution of the sample mean.

Accepted Answer

The answer of Examination Times Narrative
The time necessary to complete...

Question 5

Examination Times Narrative
The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed.
-Refer to Examination Times Narrative. What is the mean of the sampling distribution of  ?

Accepted Answer

The answer of Examination Times Narrative
The time necessary to complete...

Question 6

Examination Times Narrative
The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed.
-Refer to Examination Times Narrative. Can we say that the sampling distribution of  is approximately normally distributed? Why?

Accepted Answer

The answer of Examination Times Narrative
The time necessary to complete...

Question 7

Average Newborn Weights Narrative
It is known that the birth weight of newborn babies in Canada has a mean of 3.20 kg with a standard deviation of 0.80 kg. Suppose we randomly sample 64 birth certificates and record the birth weights of these babies.
-Refer to Average Newborn Weights Narrative. Find the mean and standard deviation of the sampling distribution of  .

Accepted Answer

The answer of Average Newborn Weights Narrative
It is known that...

Question 8

Food Expenditures Narrative
The amount of money spent on food per week by a Canadian family is known to have a mean of $92 and a standard deviation of $9. Suppose a random sample of 81 families is taken and their sample mean food expenditure is calculated.
-Refer to Food Expenditures Narrative. Completely describe the sampling distribution of the sample mean,  .

Accepted Answer

The answer of Food Expenditures Narrative
The amount of money spent...

Question 9

Department Store Audits Narrative
An auditor is going to sample 64 charge accounts from the many active accounts at a large department store. Suppose the average balance owed among all the store's accounts is $75 with a standard deviation of $100.
-Refer to Department Store Audits Narrative. What is the probability the sample mean of the balances owed among the 64 accounts sampled by the auditor is below $70?

Accepted Answer

The answer of Department Store Audits Narrative
An auditor is going...

Question 10

Examination Times Narrative
The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed.
-Refer to Examination Times Narrative. If the sample mean,  , is actually 50 minutes, what can be said about the claim that $\mu$ = 52?

Accepted Answer

The answer of Examination Times Narrative
The time necessary to complete...

Question 11

Miller Analogies Test Narrative
Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 100 students applied for entrance into graduate school in physics.
-Refer to Miller Analogies Test Narrative. Find the mean and standard deviation of the sampling distribution of  .

Accepted Answer

The answer of Miller Analogies Test Narrative
Graduate students applying for...

Question 12

Average Newborn Weights Narrative
It is known that the birth weight of newborn babies in Canada has a mean of 3.20 kg with a standard deviation of 0.80 kg. Suppose we randomly sample 64 birth certificates and record the birth weights of these babies.
-Refer to Average Newborn Weights Narrative. What is the probability the sample mean birth weight as recorded on the birth certificates will be less than 3.125 kg?

Accepted Answer

The answer of Average Newborn Weights Narrative
It is known that...

Question 13

The distribution of scores for the 1000 final exams in a statistics course has a mean of 74 and a standard deviation of 15. A random sample of 36 exam papers is selected. What is the probability that the sample mean is higher than 77?

Accepted Answer

The answer of The distribution of scores for the 1000...

Question 14

Department Store Audits Narrative
An auditor is going to sample 64 charge accounts from the many active accounts at a large department store. Suppose the average balance owed among all the store's accounts is $75 with a standard deviation of $100.
-Refer to Department Store Audits Narrative. Find the mean and standard deviation of the sampling distribution of  .

Accepted Answer

The answer of Department Store Audits Narrative
An auditor is going...

Question 15

Lab Mice Experiments Narrative
In a learning experiment, untrained mice are placed in a maze and the time required for each mouse to exit the maze is recorded. The average time for untrained mice to exit the maze is $\mu$ = 50 seconds and the standard deviation of their times is $\sigma$ = 16 seconds. Suppose that a sample of 64 randomly selected untrained mice are placed in the maze and the time necessary to exit the maze is recorded for each.
-Refer to Lab Mice Experiments Narrative. Find the mean and standard deviation of the sampling distribution of  .

Accepted Answer

The answer of Lab Mice Experiments Narrative
In a learning experiment,...

Question 16

Examination Times Narrative
The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed.
-Refer to Examination Times Narrative. What is the standard deviation of the sampling distribution of  ?

Accepted Answer

The answer of Examination Times Narrative
The time necessary to complete...

Question 17

IQ of Elementary School Children Narrative
In a particular large school system, the average IQ of elementary school children is 105 and the standard deviation is 15. A sample of 81 children is randomly selected from elementary schools within the system.
-Refer to IQ of Elementary School Children Narrative. What is the probability that the average IQ of this sample is below 108?

Accepted Answer

The answer of IQ of Elementary School Children Narrative
In a...

Question 18

IQ of Elementary School Children Narrative
In a particular large school system, the average IQ of elementary school children is 105 and the standard deviation is 15. A sample of 81 children is randomly selected from elementary schools within the system.
-Refer to IQ of Elementary School Children Narrative. Find the mean and standard deviation of the sampling distribution of  .

Accepted Answer

The answer of IQ of Elementary School Children Narrative
In a...

Question 19

Examination Times Narrative
The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed.
-Refer to Examination Times Narrative. What is the probability this sample produces an average of less than 50 minutes?

Accepted Answer

The answer of Examination Times Narrative
The time necessary to complete...

Question 20

Miller Analogies Test Narrative
Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 100 students applied for entrance into graduate school in physics.
-Refer to Miller Analogies Test Narrative. Find the probability that the average score of this group of students is higher than 76.

Accepted Answer

The answer of Miller Analogies Test Narrative
Graduate students applying for...

Quiz 7: Sampling Distributions

A fair die is rolled. If the top face is a 5 or 6, you win $1; otherwise you win nothing. Let be the amount you win in one play of the game and let be the average amount you win in two plays of the game. Find the sampling distribution of .

The distribution of scores for the 1000 final exams in a statistics course has a mean of 74 and a standard deviation of 15. A random sample of 36 exam papers is selected. What is the probability that the sample mean is higher than 77?