13.69 Horseshoe crabs and width A study of horseshoe crabs found a logistic regression equation for predicting the probability that a female crab had a male partner nesting nearby by using x = width of the carapace shell of the female crab (in centimeters). The results were Term Coef Constant −12.351 Width 0.497

a. For width, Q1 = 24.9 and Q3 = 27.7. Find the estimated probability of a male partner at Q1 and at Q3. Interpret the effect of width by estimating the increase in the probability over the middle half of the sampled widths.

b. At which carapace shell width level is the estimated probability of a male partner (i) equal to 0.50, (ii) greater than 0.50, and (iii) less than 0.50?