Question

An investigator is interested in the wages of married couples living in Scotland.She knows that the hourly wages of wives are normally distributed with a mean of £15 and a standard deviation of £2. The hourly wages of husbands are normally distributed with a mean of £20 and a standard deviation of £3. If there is a positive covariance of 2.0 between the wages of husbands and wives, for what proportion of married couples will the husband earn at least £2 per hour more than the wife?

		0.84
		0.16
		0.09
		0.91
		0.63

Answer 1

Let W denote wife and H husband,

The the distribution of difference of wages per hour between Husband and wife is normally distributed with mean

and standard deviation

Define the standard random Z as

The the proportion of married couples will the husband earn at least £2 per hour more than the wife is

So, the required proportion is 0.84