Question

Dr. Jones has found that, over the years, 95% of the babies she has delivered weighed x pounds, where | − 8.2| − 1.5 ≤ 0. (SLO #2) 1. Solve the inequality. Show your work. 2. Interpret the meaning of your answer to part (a) in the context of this problem. 3. How likely (or unlikely) would it be for the next baby Dr. Jones delivers to weigh 6 pounds 5 ounces? Explain.

Answer 1

Part 1.

Given inequality is = |x−8.2|−1.5≤0

Adding 1.5 to both sides

|x−8.2|−1.5+1.5 ≤ 0+1.5

Simplifying this we get

|x−8.2| ≤ 1.5

Again simplifying we have,

x-8.2 ≤ 1.5 or x-8.2≥ -1.5

Solving x-8.2 ≤ 1.5 we get , x ≤ 9.7

And

Solving x-8.2≥ -1.5 we have , x ≥ 6.7

Now combining the ranges we get,

6.7≤ x ≤9.7

Part 2.

This range defines that the babies delivered weigh between 6.7 and 9.7 pounds.

Part 3.

It is unlikely that the next baby born will weigh 6 pounds and 5 ounces as 95% babies weigh more than 6.5 pounds and range lies between 6.7 and 9.7.