Question

Do Americans work more than the French? American adults work on average 43.5 hours per week with a standard deviation of 4.6 hours. French adults work an average of 36 hours per week with a standard deviation of 5.1 hours.

3. A random sample of 110 Americans and 135 French adults were selected and surveyed about their work time. What is the probability that the sample mean for French is greater than that of the Americans?​

Answer 1

To determine the probability that the sample mean for French is greater than that of the Americans, we need to use the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will become more and more normal, regardless of the distribution of the population from which the samples are drawn.

So, we can assume that the sample means of both American and French adults will be normally distributed with a mean of 43.5 hours/week and 36 hours/week respectively and a standard deviation of 4.6/sqrt(110) and 5.1/sqrt(135) respectively.

We can use these assumptions and the Z-score formula to find the probability that the sample mean for French is greater than that of Americans.

Z = (36 - 43.5) / (sqrt((4.6/sqrt(110))^2 + (5.1/sqrt(135))^2))

The resulting Z-score will be negative, meaning that the probability that French sample mean is greater than American sample mean is low and it's a rare event.