W. Duellman and J. Kohler explore a new species of frog in the article "New Species of Marsupial Frog (Hylidae: Hemiphractinae: Gastrotheca) from the Yungas of Bolivia" (Journal of Herpetology, Vol. 39, No. 1, pp. 91-100). These two museum researchers collected information on the lengths and widths of different body parts for the male and female Gastrotheca piperata. Thumb length for the female Gastrotheca piperata has a mean of 6.71 mm and a standard deviation of 0.67 mm. Let x denote thumb length for a female specimen.
a. Find the standardized version of x.
b. Determine and interpret the z-scores for thumb lengths of 5.2 mm and 8.1 mm. Round your answers to two decimal places.