X5.3.42-T Question Help A study of green sea turtles discovered that the curved
ID: 2925756 • Letter: X
Question
X5.3.42-T Question Help A study of green sea turtles discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean 55.7 standard deviation 11.8 centimeters centimeters and a. The minimum and maximum size limits for captured turtles in the legal marine turtle fishery are 40 cm and 61 cm, respectively. How lkely are you to sea turtle that is considered illegal? b. What maximum limit, L should be set so that only 10% of the turtles captured have shell lengths greater than L? capture a green a. The probability of catching a geen turtle that is considered illegal Round to three decimal places as needed)Explanation / Answer
Mean is 55.7 and s is 11.8. z can be found as (x-mean)/s
a) P(40<x<61)=P((40-55.7)/11.8<z<(61-55.8)/11.8)=P(-1.33<z<0.44)=P(z<0.44)-P(z<-1.33) or P(z<0.44)-(1-P(z<1.33))
from normal distribution table can be found as 0.67-(1-0.9082)=0.5782
b) this means we need to find the value at bottom 90% or 0.9 from the normal distribution table. it can be seen that the closest value to 0.9 is 0.9987 which has corresponding z value of 1.28 from leftmost column and top most row
thus answer is mean+z*s =55.7+1.28*11.8=70.804
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