Z-Scores and Normal Distribution Concepts

The video tutorial explains how to design aircraft seats to fit 90% of males by calculating the 90th percentile of hip widths, which are normally distributed with a mean of 13.9 inches and a standard deviation of 0.8 inches. The process involves finding the z-score for the 90th percentile using StatCrunch and then calculating the corresponding hip width using the z-score, mean, and standard deviation. The final result is a hip width of 14.9 inches, which separates the smallest 90% from the largest 10% of the male population.

Why is it not feasible to design aircraft seats to accommodate 100% of males?

• It would require seats that are too narrow.

• It would require seats that are too tall.

• It would require seats that are too short.

• It would require seats that are too wide and expensive.

What is the mean hip breadth of males according to the normal distribution?

• 14.5 inches

• 13.9 inches

• 15.2 inches

• 12.8 inches

What is the standard deviation of male hip breadths in the given distribution?

• 1.0 inches

• 0.5 inches

• 1.2 inches

• 0.8 inches

What is the significance of the mean in a normal distribution?

• It is the midpoint of the data.

• It is the most frequently occurring value.

• It is the value that separates the top 50% from the bottom 50%.

• It is the average of all data points.

What does a standard deviation of 0.8 inches indicate?

• The data points are spread out over a wide range.

• The data points are close to the mean.

• The data points are evenly distributed.

• The data points are skewed to the right.

What does the 90th percentile represent in this context?

• The hip breadth that is smaller than 90% of the population.

• The hip breadth that is larger than 10% of the population.

• The average hip breadth of the population.

• The hip breadth that is larger than 90% of the population.

What is the area under the normal curve to the left of the 90th percentile?

• 0.5000

• 0.9000

• 0.1000

• 0.7500

What does the area of 0.9000 under the curve represent?

• The area at the median.

• The area to the right of the 90th percentile.

• The area to the left of the 90th percentile.

• The area at the mean.

What tool is used to find the z-score corresponding to the 90th percentile?

• R

• Python

• StatCrunch

• Excel

What is the z-score for the 90th percentile in this problem?

• 0.84

• 1.28

• 2.33

• 1.96