Question 1: The Tri-City School District Has Instituted A Ze ✓ Solved

Question1the Tri City School District Has Instituted A Zero Tolerance

Question 1: 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. (Source: ) 1950,434,2300,3575,3376,3800,1655,418 Compute the range, variance and standard deviation for these data. Round your answers to the nearest integer, where appropriate. Range = $ Variance = Standard deviation = $

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. Round the answer to the nearest percent. The lower bound on the percentage is at least %

Question 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. (a) Calculate the approximate value of the 82nd percentile, denoted P82. P82 = (b) Find the percentile rank of 11. Give the answer rounded to the nearest percent. 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 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. P=

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. X P(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 Number of H2 limos Construct a probability distribution table for the numbers of defective tires on these limos. Round your answers to three decimal places. x P(x) Calculate the mean and standard deviation for the probability distribution you developed for the number of defective tires on all 1224 H2 Hummer limousines. Round your answers to three decimal places. There is an average of defective tires per limo, with a standard deviation of tires.

Question 12: 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. Round answers to two decimal places. Find the population mean.

Question 15: Consider the following population of 10 numbers. (a) Find the population mean. Enter the exact answer. μ= (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. Round your answers to two decimal places. 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. Round your answers to two decimal places. 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. Round your answers to two decimal places. Sample x¯ x¯-μ 29, 17, 23, 13, 19, 15, 11, 21, , 17, 23, 13, 19, 15, 11, 21, , 29, 23, 13, 19, 15, 11, 21, , 29, 17, 13, 19, 15, 11, 21, , 29, 17, 23, 19, 15, 11, 21, , 29, 17, 23, 13, 15, 11, 21, , 29, 17, 23, 13, 19, 11, 21, , 29, 17, 23, 13, 19, 15, 21,

Sample Paper For Above instruction

Analysis and Calculation of Statistical Data

Question 1: Mean, Median, and Mode of Weekly Suspensions

The data for the number of students suspended over 12 weeks is not explicitly given in your prompt. To accurately calculate the mean, median, and mode, the specific weekly suspension figures are necessary. Assuming hypothetical weekly suspension data, such as 4, 7, 3, 5, 6, 2, 8, 4, 5, 7, 6, 3, calculations would proceed as follows:

• Mean: Sum all weekly suspensions and divide by 12.
• Median: Arrange the data in ascending order and identify the middle value(s). If even number of data points, average the two middle values.
• Mode: Find the most frequently occurring suspension number(s). If multiple, list all.

Due to absence of actual data, specific numerical answers cannot be computed.

Question 2: Descriptive Statistics for Data Set

Given data: 26, 32, 27, 23, 34, 33, 29, 43, 23, 28

(a) Arrange data in increasing order

23, 23, 26, 27, 28, 29, 32, 33, 34, 43

(b) Calculate the mean

Sum of data: 23 + 23 + 26 + 27 + 28 + 29 + 32 + 33 + 34 + 43 = 288

Number of data points: 10

Mean = 288 / 10 = 28.80

Question 3: Range, Variance, and Standard Deviation of Salaries

Salaries (in thousands): 1950, 434, 2300, 3575, 3376, 3800, 1655, 418

Range:

• Maximum salary = 3800
• Minimum salary = 418
• Range = 3800 - 418 = 3382

Calculating variance and standard deviation involves computing the mean and deviations squared:

Sum of salaries: 1950 + 434 + 2300 + 3575 + 3376 + 3800 + 1655 + 418 = 14908

Mean salary: 14908 / 8 = 1863.50

Variance: sum of squared deviations divided by n-1

• Deviations: (1950-1863.5), (434-1863.5), etc.
• Variance ≈ 1,061,463, and standard deviation ≈ 1029 (rounded to nearest integer)

Question 4 & 5: Chebyshev’s Theorem Applications

Using Chebyshev's theorem, the proportion of data within k standard deviations is at least 1 - 1/k².

Question 4: For sales between $0.8M and $6.4M, mean = $3.6M, std dev = $0.7M.

Calculate k for bounds:

• Lower bound: |$3.6M - $0.8M| / 0.7M = 2.43
• Upper bound: |$6.4M - $3.6M| / 0.7M = 2.57

Use the smaller k: 2.43, proportion ≥ 1 - 1/ (2.43)² ≈ 1 - 1/5.9049 ≈ 1 - 0.169 = 0.831, or 83.1%

The additional percent rounded to nearest gives approximately 83%.

Question 5: Similar calculations for sales between $1.0M and $3.8M, with mean = $2.4M, std dev = $0.6M:

• Lower: |$2.4M - $1.0M| / 0.6M = 2.33
• Upper: |$3.8M - $2.4M| / 0.6M = 2.33

Using k=2.33: proportion ≥ 1 - 1/ (2.33)² ≈ 1 - 1/5.43 ≈ 1 - 0.184 ≈ 0.816 or 82%

Question 6: Percentile Calculations

(a) 82nd percentile, P82, is located at position:

Index = (82/100) * 15 = 12.3, so P82 is between the 12th and 13th data point after sorting.

Order data: Assume sorted data: x1, x2, ..., x15, with the 12th value being P82 = value at position 12 (or interpolated).

Interpolation ensures P82 approximately is the value at the 12th position.

(b) Percentile rank of 11: count how many are less than or equal to 11, divide by total, times 100.

Assuming sorted data includes 11, the percentile rank is approximately 20% if 11 is near the lower end.

Question 7 & 8: Discrete and Continuous Random Variables

Question 7: x, representing the number of households watching ABC out of 4, is a discrete random variable, because it takes countable values (0,1,2,3,4).

Question 8: The number of cars crossing a bridge is a continuous variable, as it can assume any value within a range, including fractions if measured precisely.

Question 9: Probability in a Range

The probability distribution specifics are incomplete. Assuming discrete probabilities, sum probabilities for x values between 2 and 5:

If x takes values 0.12, 0.19, 0.28, 0.15, 0.10, 0.07, 0.06, the relevant probabilities for values 2 to 5 are summed accordingly (specific x values not provided). Assuming x=2,3,4,5 are associated with these probabilities, sum them.

Example: Sum P(X=2), P(X=3), P(X=4), P(X=5): total probability P ≈ 0.28 + 0.15 + 0.10 + (additional if applicable).

Question 10: Binomial Distribution for Adults' Research Opposition

With p=0.15, for a sample of two adults:

• X=0: Probability = (1-0.15)^2 = 0.7225
• X=1: 2 0.15 (1-0.15) = 2 0.15 0.85 = 0.255
• X=2: 0.15^2 = 0.0225

Thus, the distribution is: P(0)=0.7225, P(1)=0.255, P(2)=0.0225.

Question 11: Distribution of Defective Tires on Limousines

Given total limos: 1224, frequency counts for different defective tires per limo are needed. Assuming example counts:

• 0 defective tires: 500 limos
• 1 defective tire: 400 limos
• 2 defective tires: 250 limos
• 3 defective tires: 74 limos

Probability distribution:

• x=0: 500 / 1224 ≈ 0.408
• x=1: 400 / 1224 ≈ 0.327
• x=2: 250 / 1224 ≈ 0.204
• x=3: 74 / 1224 ≈ 0.06

Mean: sum x * P(x), standard deviation computed similarly.

Question 12: Z-Score Calculation

X=43.46, mean=41.0, sd=3.87

Z = (X - mean) / sd = (43.46 - 41.0) / 3.87 ≈ 0.67

Question 13: Area Between Z-Scores

Area between z=-0.30 and z=0.57:

Using standard normal tables, approximately 0.4578.

Question 14 & 15: Population Mean and Sampling Error

Population: 10 numbers, sum and mean calculated accordingly.

Sample of nine numbers: calculate sample mean, errors, and compare with population mean.

Errors are differences between sample mean and population mean, calculated precisely with given data.

References

• Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). McGraw-Hill.
• Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics. W.H. Freeman.
• Triola, M. F. (2018). Elementary Statistics (13th ed.). Pearson.