Show that for a sample of n=33, the smallest and largest Z-values are minus 1.89

Question

Show that for a sample of n=33, the smallest and largest Z-values are minus 1.89 and plus1.89 and the middle (that is,17th)Z-value is 0.00.

With 33 observations, the smallest of the standard normal quantile values covers an area under the normal curve of StartFraction Blank Over 34 EndFraction equals? The corresponding Z-value is minus 1.89. The largest of the standard normal quantile values covers an area under the normal curve of StartFraction Blank Over 34 EndFraction equals? The corresponding Z-value is plus 1.89. The middle of the standard quantile values covers an area under the normal curve of StartFraction Blank Over 34 EndFraction equals? The corresponding Z-value is 0.00. (Type integers or decimals rounded to four decimal places as needed.)

Explanation / Answer

With 33 observations, the smallest of the standard normal quantile values covers an area under the normal curve of 1/34 equals 0.0294 The corresponding Z-value is minus 1.89. The largest of the standard normal quantile values covers an area under the normal curve of 33/34 equals 0.9706 The corresponding Z-value is plus 1.89. The middle of the standard quantile values covers an area under the normal curve of 17/34 equals 0.5000 The corresponding Z-value is 0.00.

This is because,

P(Z<-1.89) = 0.0294 = 1/34

P(Z<1.89) = 0.9706 = 33/34

P(Z<0) = 0.5000 = 17/34

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