6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
2:14 minutesProblem 3.CRE.7
Textbook Question
Normal Distribution Examine the distribution shown in the histogram from Exercise 6. Does it appear that the sample data are from a population with a normal distribution? Why or why not?
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Step 1: Observe the histogram provided. A normal distribution typically has a bell-shaped curve, where the frequencies are highest at the center and taper off symmetrically towards the tails. In this histogram, the frequencies do not follow this pattern.
Step 2: Note the peaks and troughs in the histogram. For a normal distribution, the frequencies should gradually decrease as you move away from the center. However, the histogram shows irregular peaks, such as the high frequency at digit 5 and lower frequencies at digits 3 and 4.
Step 3: Assess the symmetry of the distribution. A normal distribution is symmetric around its mean. In this histogram, the frequencies are not symmetric; for example, the frequencies for digits 0, 1, and 2 differ significantly from those for digits 7, 8, and 9.
Step 4: Consider the spread of the data. A normal distribution has a smooth, continuous spread. The histogram here shows a jagged pattern with abrupt changes in frequency, which is inconsistent with a normal distribution.
Step 5: Conclude based on the observations. The irregular shape, lack of symmetry, and uneven spread of frequencies suggest that the sample data are not from a population with a normal distribution.
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