Questions: An average of many different studies of handedness indicate that in a random sample of adults, 14 percent of men are left-handed and 6 percent of women are left-handed. (Assume the rest are right-handed.) Suppose you have a sample of 250 women and 200 men, in which the numbers of left-handed and right-handed people reflect the average percentages. Make a two-way table that shows the distribution you would find. Fill out the two-way table below. Women Men -------------------------- Right-Handed Left-Handed (Simplify your answers.)

Solution Steps

To solve this problem, we need to calculate the number of left-handed and right-handed individuals in the given sample of men and women based on the provided percentages. For women, 6% are left-handed, so 94% are right-handed. For men, 14% are left-handed, so 86% are right-handed. We will use these percentages to find the actual numbers in the sample of 250 women and 200 men.

To find the number of left-handed women, we use the percentage given: \(6\%\) of 250 women. This is calculated as: \[ \text{Left-Handed Women} = 250 \times \frac{6}{100} = 15 \]

The remaining women are right-handed. Since \(100\% - 6\% = 94\%\), we calculate: \[ \text{Right-Handed Women} = 250 \times \frac{94}{100} = 235 \]

Similarly, for men, \(14\%\) of 200 men are left-handed. This is calculated as: \[ \text{Left-Handed Men} = 200 \times \frac{14}{100} = 28 \]

The remaining men are right-handed. Since \(100\% - 14\% = 86\%\), we calculate: \[ \text{Right-Handed Men} = 200 \times \frac{86}{100} = 172 \]

Final Answer