Compared to their stay-at-home peers, women employed outside the home have higher levels

Chapter 1, Problem 1.30

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Compared to their stay-at-home peers, women employed outside the home have higher levels of high-density lipoproteins (HDL), the good cholesterol associated with lower risk for heart attacks. A study of cholesterol levels in 2000 women, aged 2564, living in Augsburg, Germany, was conducted by Ursula Haertel, Ulrigh Keil, and colleagues2 at the GSF-Medis Institut in Munich. Of these 2000 women, the 48% who worked outside the home had HDL levels that were between 2.5 and 3.6 milligrams per deciliter (mg/dL) higher than the HDL levels of their stayat-home counterparts. Suppose that the difference in HDL levels is normally distributed, with mean 0 (indicating no difference between the two groups of women) and standard deviation 1.2 mg/dL. If you were to select an employed woman and a stay-at-home counterpart at random, what is the probability that the difference in their HDL levels would be between 1.2 and 2.4?