16   6 Caroline runs a hairdressing salon in London. She reads the following article. How much hair loss is normal in a day According to the American Academy of Dermatologists, an adult will normally lose anywhere from 50 to 100 strands of hair per day. For people with longer hair strands, losing them may be more noticeable. Since there are 100,000 hair follicles – or more – on each person’s scalp, the loss of 100 or so hair strands a day doesn’t make a big difference in appearance. Average hair loss in men and women Women tend to lose more hair strands per day than men. There’s no way to measure the difference objectively, because daily heat styling and frequent hair colouring plays a big part in how much of your hair sheds. Approximately 40 percent of women lose extra hair every day because of the way they style it. What causes hair to fall out Some daily hair loss is normal. Increased hair loss can be a result of stress or a health condition. [Source: https://www.healthline.com/health/how-much-hair-loss-is-normal] Caroline states that the random variable X ~ B(100 000, 0.001) could be used to model the number of hairs lost by a randomly selected customer during one day. (a) Explain how Caroline chose her parameters for the distribution of X (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (b) Comment on the assumptions underlying Caroline’s model indicating whether or not these are reasonable. Your answer should include three different statements. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 17   Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 5 marks)