(complete parts a-e) A study finds that the carapace length of an adult spider is normally distributed with a mean of 17.98 mm and a standard deviation of 1.74 mm. Let x denote carapace length for the adult spider.

a. Sketch the distribution of the variable x.

b. Obtain the standardizedversion, z, of x.

c. Identify and sketch the distribution of z.

d. Find thez-scores that correspond to the percentage of adult spiders that have carapace lengths between 15 mm and 16mm. The percentage of adult spiders that have carapace lengths between 15 mm and 16mm is equal to the area under the standard normal curve between _____ and _____ (fill the blanks)

e. Find thez-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 20 mm. The percentage of adult spiders that have carapace lengths exceeding 20 mm is equal to the area under the standard normal curve that lies to the right of ______ (round to two decimal places).