4. The life span of a particular species of turtle in captivity is normally distributed prith a mean Iife span of 180 years and a standard deviation of 40 years. a) Sketch the normally distributed curve to illustrate the standard deviations. b) $68 \%$ of all turtles have a lifespan between what age range? c) $95 \%$ of all turtles have a lifespan between what age range? d) What percent of turiles will live more than 220 years? e) What percent of turtles will live more than 260 years?

Step 1 ：a) Sketch the normally distributed curve with a mean of 180 years and a standard deviation of 40 years.

Step 2 ：b) Since 68% of the data falls within 1 standard deviation of the mean, the age range is \(180 - 40 = 140\) years to \(180 + 40 = 220\) years.

Step 3 ：c) Since 95% of the data falls within 2 standard deviations of the mean, the age range is \(180 - 2(40) = 100\) years to \(180 + 2(40) = 260\) years.

Step 4 ：d) To find the percentage of turtles living more than 220 years, we look at the area to the right of 220 on the normal curve. This is 1 standard deviation above the mean, so approximately 16% of turtles will live more than 220 years.

Step 5 ：e) To find the percentage of turtles living more than 260 years, we look at the area to the right of 260 on the normal curve. This is 2 standard deviations above the mean, so approximately 2.5% of turtles will live more than 260 years.