Question: If z is the positive number such that the interval within z standard deviations of the mean contains 50% of a normal distribution, then a.

If z is the positive number such that the interval within z standard deviations of the mean contains 50% of a normal distribution, then
a. Explain why this value of z is about 0.67.
b. Explain why for any normal distribution the first and third quartiles equal μ - 0.67σ and μ + 0.67σ.
c. The interquartile range, IQR, relates to σ by IQR = 2 × 0.67σ. Explain why.

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