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Z-Scores and Normal Distribution Concepts

Z-Scores and Normal Distribution Concepts

Assessment

Interactive Video

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

Created by

Thomas White

FREE Resource

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.

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20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

0.5000

0.9000

0.1000

0.7500

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