Answer: Mexican Fan Palm (Washingtonia robusta) tolerates salty soil, constant southeast wind, storm winds, salt spray and occasional sand blasting so what you describe is not normal for this plant. It's normal for the oldest leaves to yellow and then turn brown (these should be pruned off when they're completely brown) but the new foliage should remain green. If the new leaves are yellowing, it's either a problem with watering, or your plant needs to be fed. Palms are very susceptible to nutrient deficiencies of nitrogen, potassium, magnesium and manganese. Symptoms include yellowing, streaking or even spotting of the fronds. Following a regular, balanced fertilization program for palms is important to avoid these problems. As for watering, apply water slowly so it wets the entire root mass, then allow the top inch of soil to dry out before thoroughly watering again.
Best wishes with your new palms.
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