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Match each of the descriptions on the left with the correct lettered terms on the right. Each letter is used once, or not at all. ( 2 points each ) ____ A continuous probability distribution A. Census for which the probability that the random B. Standard Error variable takes a value in an interval is the C. Uniform same for equal-length intervals. D. Statistic ____ A result that says that X may be treated E. Sample like a normal random variable under F. Normal certain conditions. G. Point Estimator ____ A number that describes some trait, H. Sampling Distribution or feature, of a population. I. Parameter ____ A data set made up of observations J. Central Limit Theorem on every element in the population. K. Z-number ____ A probability distribution whose primary defining characteristic is a symmetric, bell-shaped curve. ____ A probability distribution for a sample statistic. ____ A normal random variable minus its mean, divided by its standard deviation.

The mean hourly pay rate for financial managers in the East North Central region is $25.85, and the standard deviation is $5.05. Assume that pay rates are normally distributed. What hourly rate separates the bottom 12% of pay rates from the upper 88% of pay rates for these financial managers? ( 10 points )

Each sample statistic on the left is used as a point estimator of one of the population parameters on the right. Match them up correctly. Each letter is used once, or not at all. ( 2 points each ) ____ X A. p B. s ____ p C. m D. q ____ s E. l

A recent survey of MBA graduates revealed that their mean salary was $90,000, with a standard deviation of $9,500. If a simple random sample of 35 MBA graduates is to be taken: ( 5 points each )

a. What is the probability that the sample mean salary will exceed $92,500?

b. What is the probability that the sample mean salary will fall between $85,000 and $91,500?

Given that z is the standard normal random variable, find z for each situation: ( 5 points each )

a. The area to the left of z is 0.7019.

b. The area between -z and z is 0.8294.

A population has a mean of 100 and a standard deviation of 15. A simple random sample of size 50 will be taken and the sample mean will be used to estimate the population mean. Specify the sampling distribution of X. ( 5 points )

If the population proportion is 0.7, and a simple random sample of size 65 will be taken: ( 5 points )

a. Specify the sampling distribution of p, the sample proportion.

b. What is the probability that the sample proportion will take a value between 0.65 and 0.83?

Given that z is the standard normal random variable, sketch the appropriate figure that accompanies each probability (complete with the appropriate shading to represent the probability), and compute the following probabilities: ( 5 points each )

a. ![−1.789

b. ![z ≥ 1.55]

c. ![−2.07 > z]

A business executive has just been transferred from Chicago to Atlanta and needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes that the price she will get by leaving her house on the market for another month is uniformly distributed between $200,000 and $225,000.

a. Sketch the graph of the pdf. ( 5 pts )

b. If she leaves her house on the market for another month, what is the probability that she will get at least $215,000 for it? ( 5 pts )

c. If she leaves her house on the market for another month, what is the probability that it will sell for less than $210,000? ( 5 pts )

d. Should she leave the house on the market for another month, or accept her employer’s offer to buy the house now? EXPLAIN YOUR REASONING ( 5 pts )

Paper For Above instruction

The assignment encompasses a series of statistical problems and conceptual questions designed to evaluate understanding of probability distributions, sampling distributions, point estimators, and decision-making based on statistical data. The initial task involves matching descriptions of statistical terms with their corresponding definitions, requiring comprehension of concepts such as continuous probability distributions, standard error, and normal distribution. The subsequent questions focus on applying knowledge of normal distribution to determine cutoff rates for pay rates and analyzing sample statistics with respect to population parameters. This includes calculating probabilities related to sample means and proportions, utilizing the standard normal distribution (z-scores), and interpreting graphical representations of normal curves. Furthermore, the assignment includes practical decision-making scenarios, such as evaluating the expected selling price of a house modeled by a uniform distribution, and determining whether to accept an immediate purchase offer or wait for a potentially higher bid. The final questions emphasize the integration of theoretical understanding with real-world applications, requiring calculations, graphical sketches, and rationale-based decision explanations.

Matching statistical terms to their definitions is fundamental for understanding the core concepts in statistics. For example, the continuous probability distribution (A) refers to a distribution where the probability that a variable falls within an interval is uniform across equal-length intervals, characteristic of the uniform distribution. The standard error (B) represents an estimate of the standard deviation of a sampling distribution, crucial for inference. The concept of a normal distribution (F) depicts a symmetric, bell-shaped curve that is fundamental in statistical inference, especially under the Central Limit Theorem, which states that the distribution of sample means approaches normality as sample size increases.

In the practical applications, understanding how to determine cutoff points in a normal distribution enables decision-makers to evaluate thresholds for pay rates, for instance, identifying the hourly wage that separates the lowest 12% from the rest, involving inverse normal calculations. Similarly, analyzing sample means and proportions involves deriving the sampling distribution, calculating standard errors, and applying the z-score formula to compute probabilities. For example, in assessing whether the average salary exceeds a certain amount, the sampling distribution's standard deviation (standard error) is derived from the population standard deviation divided by the square root of the sample size, following the properties of the normal distribution.

The questions involving graphical interpretation of z-scores and their corresponding areas under the normal curve are topics of fundamental importance in inferential statistics. These require knowledge of standard normal tables or calculator functions to translate area probabilities into z-values and vice versa. Such skills are essential in hypothesis testing and confidence interval construction.

Furthermore, the applications extend to real estate valuation, where the uniform distribution models the range of potential house prices. Calculating the probability of a house selling at or above a specific price requires understanding the shape and properties of the uniform distribution, including the uniform probability density function (pdf). The decision on whether to wait or accept an immediate offer involves comparing expected values and considering the financial implications based on the modeled distribution. These decision-making processes exhibit a blend of statistical theory and practical reasoning, reflecting critical competencies in data-driven business strategies.

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