Which would you expect to have a density curve that is higher at the mean: the standard normal distribution or a normal distribution with standard deviation 0.5? Explain.

Which would you expect to have a density curve that is higher at the mean: the standard normal distribution or a normal distribution with standard deviation 0.5? Explain.

Question
Normal distributions
asked 2020-11-17
Which would you expect to have a density curve that is higher at the mean: the standard normal distribution or a normal distribution with standard deviation 0.5? Explain.

Answers (1)

2020-11-18
The curve is in the form of normal distribution if it is bell shaped and symmetric and the curve is called the density curve which is symmetric, and centered around its mean and the spread is determined by its standard deviation.
The uniform continuous distribution is the curve in which all the intervals have same length and the standard deviation for this curve must be | or less than 1, which means the variance of uniform continuous distribution is less than 1.
The height of density curve with standard deviation is higher around mean in normal distribution because it became narrow around the mean whereas the graph of uniform continuous distribution represents uniformity in all interval.
Thus, the standard normal distribution has higher density curve at the mean than uniform distribution.
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