Exam 1 Covers Chapters 1–5 Math 140 Spring 2015 Csun

Exam 1 Covers Chapters 1 5 Math 140spring 2015 Csun Show All Wor

Analyze and solve the mathematical and statistical problems related to descriptive statistics, probability distributions, hypothesis testing, and data analysis based on the exam content from Math 140 Spring 2015 at CSUN, covering chapters 1-5. Show all work clearly with explanations to demonstrate understanding of concepts such as sampling methods, distribution construction, z-scores, measures of center and variability, outlier detection, probability calculations, and data interpretation.

Paper For Above instruction

The exam from Math 140 at CSUN, Spring 2015, encompasses fundamental topics from chapters 1 through 5, focusing on understanding and applying statistical concepts through various problems. The tasks involve defining key terms, constructing frequency distributions, calculating descriptive statistics, analyzing distributions, understanding probability, and interpreting data visualizations such as histograms and pie charts.

First, the definition of a stratified random sample emphasizes its structure as a sampling method where the population is divided into subgroups or strata, and samples are randomly selected from each stratum proportionally or equally, ensuring representation across all segments. This technique enhances the accuracy and reliability of statistical inferences by accounting for variability within the population.

The data provided concerning the cash carried by students offers an opportunity to construct a relative frequency distribution with class intervals starting at 1 and a class width of 6. Accurate frequency counts within each class are essential, followed by calculating relative frequencies, which are obtained by dividing class frequencies by the total number of observations. The cumulative relative frequency is then derived by sequentially summing the relative frequencies. Visual representations like histograms, which display the distribution's shape, and pie charts, illustrating proportional data segments, are useful for data interpretation. Both should employ the relative frequencies for consistency and clarity.

Regarding students’ distances from campus, the calculation of z-scores involves subtracting the population mean (10 miles) from individual values (14 and 20 miles) and dividing by the standard deviation (2.5 miles). The resulting z-scores quantify how many standard deviations away each value is from the mean. Values exceeding approximately 2 or -2 are generally considered unusual; thus, 14 miles, with a z-score of (14-10)/2.5 = 1.6, is somewhat unusual but not strictly outside typical variability, while 20 miles, with a z-score of (20-10)/2.5 = 4, is highly unusual and indicates an outlier.

The analysis of employees in a Hollywood movie production company involves calculating the mean and standard deviation of their ages treated as a sample. This involves summing all age values, dividing by the number of data points for the mean, and using the standard deviation formula for samples to assess age variability. The age distribution can then be characterized as skewed or symmetric based on the calculated measures, with implications for workforce demographic trends.

For the dataset provided, the five-number summary (minimum, first quartile, median, third quartile, maximum) summarizes the distribution. Outliers are identified by calculating fences—values beyond 1.5 times the interquartile range (IQR) above Q3 or below Q1. Marking these outliers on a boxplot facilitates understanding of data spread and potential anomalies.

The probability distribution question involving green-eyed children examines the binomial distribution where X represents the number of children with green eyes among four. To determine if this is a valid probability distribution, the sum of P(X) across all X values must equal 1. If valid, the mean and standard deviation are computed using binomial formulas, where the mean is np and the standard deviation is √(npq), with p being the probability of a green-eyed child.

In the case of a three-child family, finding the probability of at least two boys involves defining the sample space of all possible gender combinations, then summing probabilities for scenarios with two or more boys. This application of binomial probability reflects real-world parental strategies and family planning considerations.

Lastly, the survey data regarding adults aged 40-49 living alone introduces binomial probability calculations for independent trials. Calculating the probability that at least one individual in a sample of ten lives alone employs the complement rule, while evaluating whether this event is unusual considers the probability's size relative to common statistical thresholds. The mean and standard deviation of the binomial distribution with parameters n=10 and p=0.55 are obtained to describe the variability in the number of individuals living alone.

References

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