Frog Thumb Length. 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.