Questions: The following data lists the number of correct and wrong dosage amounts calculated by 29 physicians. In a research experiment, a group of 12 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 17 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." Complete parts (a) through (c) below. Concentration Label Correct Dosage Calculation Wrong Dosage Calculation ("1 milligram in 1 milliliter solution") 10 2 ("1 milliliter of a 1:1000 solution") 3 14 a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, and then express it as a probability. The probability of a correct dosage calculation given the bottle is labeled with a concentration is (Round to three decimal places as needed.)

The following data lists the number of correct and wrong dosage amounts calculated by 29 physicians. In a research experiment, a group of 12 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 17 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." Complete parts (a) through (c) below. Concentration Label Correct Dosage Calculation Wrong Dosage Calculation ("1 milligram in 1 milliliter solution") 10 2 ("1 milliliter of a 1:1000 solution") 3 14 a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, and then express it as a probability. The probability of a correct dosage calculation given the bottle is labeled with a concentration is (Round to three decimal places as needed.)
Transcript text: The following data lists the number of correct and wrong dosage amounts calculated by 29 physicians. In a research experiment, a group of 12 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 17 physicians was given bottles labeled with a ratio of "1 millititer of a 1:1000 solution." Complete parts (a) through (c) below. Concentration Label & Correct Dosage Calculation & Wrong Dosage Calculation ("1 milligram in 1 milliliter solution") & 10 & 2 ("1 milliliter of a 1:1000 solution") & 3 & 14 a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, and then express it as a probability. The probability of a correct dosage calculation given the bottle is labeled with a concentration is $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

To solve this problem, we need to calculate the percentage of correct dosage calculations for the group of physicians given the concentration label and then express it as a probability. This can be done by dividing the number of correct dosage calculations by the total number of dosage calculations (both correct and wrong) and then converting this fraction to a probability.

Solution Approach
  1. Identify the number of correct and wrong dosage calculations for the concentration label group.
  2. Calculate the total number of dosage calculations for this group.
  3. Compute the percentage of correct dosage calculations.
  4. Express this percentage as a probability.
Step 1: Identify the Number of Correct and Wrong Dosage Calculations

Given:

  • Correct dosage calculations: \(10\)
  • Wrong dosage calculations: \(2\)
Step 2: Calculate the Total Number of Dosage Calculations

Total dosage calculations: \[ \text{Total} = 10 + 2 = 12 \]

Step 3: Compute the Percentage of Correct Dosage Calculations

Percentage of correct dosage calculations: \[ \text{Percentage} = \frac{10}{12} = 0.8333 \]

Step 4: Express the Percentage as a Probability

The probability of a correct dosage calculation given the bottle is labeled with a concentration: \[ \text{Probability} = 0.8333 \]

Final Answer

\(\boxed{\frac{5}{6}}\)

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