Assignment
Question1:
The Tri-City School District has instituted a zero-tolerance policy for students carrying any objects that could be used as weapons. The following data give the number of students suspended during each of the past 12 weeks for violating this school policy.
Find the mean, median, and mode.
Round your answers to two decimal places, where appropriate.
Mean = Median = Mode =
Question 2:
Recall the following from section 3.1 of the text. Mean : The mean for ungrouped data is obtained by dividing the sum of all values by the number of values in the data set. Median: The median is the value of the middle term in a data set that has been ranked in increasing order. If there is an even number of data, find the average of the two middle data values. Mode: The mode is the value that occurs with the highest frequency in a data set. If there are more than one data values with the highest frequency in a data set, we will have multiple modes. If all data values have the same frequency of occurrences, then the data set has no mode.
26,32,27,23,34,33,29,43,23,28
(a) Arrange the data in increasing order:
(b) Calculate the mean. The mean =
Question 3:
The following data represent the 2011 guaranteed salaries (in thousands of dollars) of the head coaches of the final eight teams in the 2011 NCAA Men's Basketball Championship. The data represent the 2011 salaries of basketball coaches of the following universities, entered in that order: Arizona, Butler, Connecticut, Florida, Kansas, Kentucky, North Carolina, and Virginia Commonwealth.
1950,434,2300,3575,3376,3800,1655,418
Compute the range, variance and standard deviation for these data.
Question 4:
The 2011 gross sales of all firms in a large city have a mean of $3.6 million and a standard deviation of $0.7 million. Using Chebyshev′s theorem, find a lower bound on the percentage of firms in this city that had 2011 gross sales between $0.8 and $6.4 million.
Questiono 5:
The 2011 gross sales of all firms in a large city have a mean of $2.4 million and a standard deviation of $ 0.6 million. Using Chebyshev's theorem, find at least what percentage of firms in this city had 2011 gross sales of $1.0 to $3.8 million. Round your answer to the nearest whole number.
Question 6:
The following data give the weights (in pounds) lost by 15 members of a health club at the end of two months after joining the club.
5 10 8 7 24 12 5 13 11 10 21 9 8 11 18
(a) Calculate the approximate value of the 82nd percentile, denoted P82.
(b) Find the percentile rank of 11.
Question 7:
In a group of households, the national news is watched on one of the following networks - ABC, CBS, or NBC. On a certain day, four households from this group randomly and independently decide which of these channels to watch. Let x be the number of households among these four that decide to watch news on ABC. Is x a discrete or a continuous random variable?
Question 8:
Classify the following random variable as discrete or continuous.
The number of cars crossing a bridge on a given day.
Question 9:
The following table gives the probability distribution of a discrete random variable x.
X 0 1 2 3 4 5 6
P(X) 0.12 0.19 0.28 0.15 0.10 0.07 0.06
Find the probability that x assumes a value in the interval 2 to 5.
Question 10:
According to a survey, 15% of adults are against using animals for research. Assume that this result holds true for the current population of all adults. Let x be the number of adults who are against using animals for research in a random sample of two adults. Obtain the probability distribution of x.
Enter the exact answers.
Question 11:
The H2 Hummer limousine has eight tires on it. A fleet of 1224 H2 limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the frequency distribution of the number of defective tires on the 1224 H2 limos.
|
Number of defective tires
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Number of H2 limos
|
65
|
202
|
336
|
328
|
203
|
73
|
13
|
3
|
1
|
Construct a probability distribution table for the numbers of defective tires on these limos.
Calculate the mean and standard deviation for the probability distribution you developed for the number of defective tires on all 1224 H2 Hummer limousines.
There is an average of defective tires per limo, with a standard deviation of tires.
Question12:
Let x have a normal distribution with a mean of 41.0 and a standard deviation of 3.87. The z value for x = 43.46, rounded to two decimal places, is:
the tolerance is +/-2%
Question 13:
For the standard normal distribution, the area between z = -0.30 and z = 0.57, rounded to four decimal places, is:
Question 14:
Find the mean and the sampling/nonsampling error.
Consider the following population of 10 numbers.
20 25 13 19 9 15 11 7 17 30
Find the population mean.
Question 15:
Consider the following population of 10 numbers.
24 29 17 23 13 19 15 11 21 34
(a) Find the population mean.
(b) Rich selected one sample of nine numbers from this population. The sample included the numbers 24, 29, 17, 13, 19, 15, 11, 21 and 34. Calculate the sampling mean and sampling error for this sample.
The sample mean is and sampling error is for this sample.
(c) Refer to part (b). When Rich calculated the sample mean, she mistakenly used the numbers 24, 29, 17, 13, 19, 15, 21, 21 and 34 to calculate the sample mean.
Find the sampling and nonsampling errors in this case.
The sampling error is and nonsampling error is in this case.
(d) List all samples of nine numbers (without replacement) that can be selected from this population. Calculate the sample mean and sampling error for each of these samples.