Question

Choose the letter of the answer that correctly completes the sentence: a number under the horizontal bar on the right side of the check mark symbol specifies the ____.

a. roughness average
b. surface mismatch
c. sampling length
d. maximum peak next

Answer 1

The discrepancy between the theoretical probability and the empirical cumulative relative frequency arises because the former uses a normal distribution as an approximation for calculating probabilities, while the latter uses actual observed data without any distribution assumptions.

Step-by-step explanation:

The question in focus is related to statistics and probability, especially concerning the distribution and standard deviation being used to calculate probabilities. When we draw a smooth curve through the midpoints of the tops of the bars of the histogram, we are creating a continuous probability distribution that represents our data. In statistics, a smooth curve could represent the estimated probability density function for the dataset. Describing the shape involves discerning whether the distribution is symmetric, skewed, unimodal, bimodal, etc.

To approximate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators (part f), we would use the normal distribution as an approximation with the sample mean (μ) and sample standard deviation (σ) if the Central Limit Theorem justifies such approximation. If the underlying data is significantly non-normal, other distributions might be more appropriate. Nevertheless, the idea is to use the z-score to find this probability by calculating the area under the curve to the left of the specified maximum capacity.

For the cumulative relative frequency (part g), we are working with the actual empirical data. We count the number of stadiums with a capacity of less than 67,000 and divide by the total number of stadiums. This yields an empirical cumulative frequency which may not exactly match the probability obtained from the normal distribution in part f, which is theoretical and assumes normality.

The answers to parts f and g are not exactly the same because part f is based on a theoretical model (normal distribution), which is an approximation that assumes a perfect bell shape and certain mathematical properties. Part g, on the other hand, is based on the actual observed data without assuming any distribution. There might be a discrepancy between the theoretical model and the real-world data, especially if the actual data distribution does not perfectly comply with the assumptions of the theoretical model.

Answer 2

The number under the horizontal bar on the right side of the check mark symbol specifies the roughness average. Differences between probabilities in parts f and g are due to one being a model approximation and the other based on actual data.

Step-by-step explanation:

In the context of surface finish in engineering drawings, a number under the horizontal bar on the right side of the check mark symbol, which is the surface finish symbol, specifies the roughness average. The roughness average, represented by Ra, is a parameter that describes the average height of roughness component irregularities from a mean line over a specified length. It does not refer to surface mismatch, sampling length, or maximum peak.

The values provided in parts c, d, e, f, and g of the question pertain to statistical analysis, probably for a course dealing with Quality Control or statistical process control.

For part f on calculating probabilities using the normal distribution, you would apply the z-score formula and find the corresponding probability from standard normal distribution tables or using a calculator. While for part g, for determining the cumulative relative frequency, you would directly analyze the data set to find the portion of stadiums with a capacity less than 67,000.

The answers to parts f and g might differ because part f is an approximation using a normal distribution model, whereas part g is a direct observational cumulative frequency, which could include actual data irregularities and deviations not considered in the normal distribution approximation.