Question

The Uniform Distribution

*Use the following information to answer the next ten
questions in excel .* The data that follow are the square
footage (in 1,000 feet squared) of 28 homes.

1.5 | 2.4 | 3.6 | 2.6 | 1.6 | 2.4 | 2.0 |

3.5 | 2.5 | 1.8 | 2.4 | 2.5 | 3.5 | 4.0 |

2.6 | 1.6 | 2.2 | 1.8 | 3.8 | 2.5 | 1.5 |

2.8 | 1.8 | 4.5 | 1.9 | 1.9 | 3.1 | 1.6 |

The sample mean = 2.50 and the sample standard deviation =
0.8302. The distribution can be written as *X* ~
*U*(1.5, 4.5).

1 What type of distribution is this?

2. In this distribution, outcomes are equally likely. What does this mean?

3 What is the height of *f*(*x*) for the
continuous probability distribution?

4 What are the constraints for the values of *x*?

5 What is *P*(2 < *x* < 3)?

6. What is *P*(x < 3.5| *x* < 4)?

7 What is *P*(*x* = 1.5)?

8. What is the 90^{th} percentile of square footage for
homes?

9. Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet.

10 Find the theoretical mean

11 Find the theoretical standard deviation

12 How do these compare to the sample mean and standard deviation?

All must be done in Excel

Answer #1

Use the following information to answer the next ten
questions. The data that follow are the square footage (in
1,000 feet squared) of 28 homes.
1.5
2.4
3.6
2.6
1.6
2.4
2.0
3.5
2.5
1.8
2.4
2.5
3.5
4.0
2.6
1.6
2.2
1.8
3.8
2.5
1.5
2.8
1.8
4.5
1.9
1.9
3.1
1.6
The sample mean = 2.50 and the sample standard deviation =
0.8302.
The distribution can be written as X ~ U(1.5,
4.5).
Find the theoretical mean.
Find...

The data that follow are the square footage (in 1000 feet
squared) of 28 homes.
1.5
2.4
3.6
2.6
1.6
2.4
2.0
3.5
2.5
1.8
2.4
2.5
3.5
4.0
2.6
1.6
2.2
1.8
3.8
2.5
1.5
2.8
1.8
4.5
1.9
1.9
3.1
1.6
The sample mean = 2.50 and the sample standard deviation =
0.8302.
The distribution can be written as X
~ U(1.5, 4.5).
a. What type of distribution is this?
b. In this distribution, outcomes are equally likely....

Why did we not just use the Pearson correlation for the previous
item? That is, what is the Pearson correlation influenced by that
the Spearman is not?
Previous question-
Square footage (thousands)
Price of house thousands
2.7
478
2.3
328
2.3
309
1.8
298
1.9
303
2.1
466
1.4
328
1.6
385
2.1
360
2.9
374
2.2
387
2.6
452
2.1
462
1.8
436
1.9
424
0.95
308
1.3
430
1.9
449
2.2
325
1.2
358
1.4
467
1.8
489...

Data shows the times for carrying out a blood test at
Rivervalley Labs
Using Excel Plot a histogram of the data. What type of
distribution does the data appear to follow?
Construct and interpret the 95% confidence interval for the
population mean time for carrying out a blood test. Assume that the
population standard deviation is unknown.
Times for blood tests (minutes)
2.5
4.9
3.6
4.3
1.9
3.4
3.2
4.0
3.1
3.6
3.9
4.4
3.9
3.1
2.7
3.5
3.6
3.7...

Use the data in Bank Dataset to answer this question.
Construct a 95% confidence interval for the mean increase in
deposits. Note that the population standard deviation σ is not
known in this case. Instead the sample standard deviation s should
be calculated from the sample and the t distribution should be
used.
2. What is the margin of error at the 95% confidence level?
Bank Dataset of Increase in deposits. Mean is 4. Sample size is
152 customers.
4.3...

The living spaces of all homes in a city have a mean of 2500
square feet and a standard deviation of 360 square feet. Let x¯ be
the mean living space for a random sample of 20 homes selected from
this city.
Find the mean of the sampling distribution of x¯.
Enter an exact answer.
mean of x¯= square feet
Find the standard deviation of the sampling distribution of
x¯.
Round your answer to one decimal place.
standard deviation of...

The living spaces of all homes in a city have a mean 2550 of
square feet and a standard deviation of 300 square feet. Let (x) be
the mean living space for a random sample of 30 homes selected from
this city.
Find the mean of the sampling distribution of (x) .
Enter an exact answer.
mean of (x)= ????? square feet
Find the standard deviation of the sampling distribution of
(x).
Round your answer to one decimal place.
standard...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

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