Quartiles.If z is the positive number such that the interval within z tandard 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 - 0.67 and + 0.67.

c. The interquartile range, IQR, relates to a by IQR = 2 x 0.67. Explain why.

My Work:

a. It wants an interval, so 50% of the normal distribution will be between the 25th percentile and the 75th percentile. The 25th is found on the zscore table to be -0.67 and the 75th percentile is 0.67. Hence, the z value for this situation would be 0.67.

b. Due to the 50% of the data being within 0.67 above and below the mean.

c. I cannot remember why this is.