A study was performed among 40 boys in a school in Edinburgh tolook at the presence of spermatozoa in urine samples according toage [15]. The boys entered the study at 8?11 years of age and leftthe study at 12?18 years of age. A 24-hour urine sample wassupplied every 3 months by each boy. Table 10.28 gives the presenceor absence of sperm cells in the urine samples for each boytogether with the ages at entrance and exit of the study and theage at the ?rst sperm-positive urine sample. For all parts of thisquestion, exclude boys who exited this study without 1sperm-positive urine sample (i.e., boys 8, 9, 14, 25, 28, 29, 30).10.47 Provide a stem-and-leaf plot of the age at firstsperm-positive urine specimen. *10.48 If we assume that all boyshave no sperm cells at age 11 (11.0 years) and all have sperm cellsat age 18, then estimate the probability of ?rst developing spermcells at ages 12 (i.e., between 12.0 and 12.9 years), 13, 14, 15,16, and 17. *10.49 Suppose mean age at spermatogenesis = 13.67years, with standard deviation = 0.89 years and we assume that theage at spermatogenesis follows a normal distribution. Thepediatrician would like to know what is the earliest age (inmonths) before which 95% of boys experience spermatogenesis becausehe or she would like to refer boys who haven’t experiencedspermatogenesis by this age to a specialist for further follow-up.Can you estimate this age from the information provided in thispart of the problem? *10.50 Suppose we are uncertain whether anormal distribution provides a good fit to the distribution of ageat spermatogenesis. Answer this question using the results fromProblems 10.47?10.49. (Assume that the large-sample methoddiscussed in this chapter is applicable to these data.)

Age at
Boy Entrance First positive Exit Observations
1 10.3 13.4 16.7 ? ? ? ? ? ? ? ? ? ? + + ? ? ? ? + + + ? ? 2 10.012.1 17.0 ? ? ? ? ? ? ? ? + ? ? + + ? + ? ? + ? + ? ? ? ? ? + + 39.8 12.1 16.4 ? ? ? ? ? ? ? ? + ? + + ? + + + + + + ? ? + + ? + 410.6 13.5 17.7 ? ? ? ? ? ? ? ? ? ? ? + + ? ? ? + ? ? ? ? 5 9.3 12.516.3 ? ? ? ? ? ? ? ? ? ? ? ? + + ? ? ? ? + ? ? ? ? ? ? ? ? 6 9.213.9 16.2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? 7 9.615.1 16.7 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? + 8 9.2 —12.2 ? ? ? ? ? ? ? ? ? ? ? ? 9 9.7 — 12.1 ? ? ? ? ? ? ? ? ? 10 9.612.7 16.4 ? ? ? ? ? ? ? ? ? ? ? ? + ? + + + + + ? ? + + ? + 11 9.612.5 16.7 ? ? ? ? ? ? ? ? ? ? + ? ? + ? + ? ? + + + 12 9.3 15.716.0 ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + + 14 9.6 — 12.0? ? ? ? ? ? ? ? ? 16 9.4 12.6 13.1 ? ? ? ? ? ? ? ? ? ? + + + + 1710.5 12.6 17.5 ? ? ? ? ? ? ? + ? + + + + + + + + ? ? + ? ? + + 1810.5 13.5 14.1 ? ? ? ? ? ? ? ? ? ? + ? ? 19 9.9 14.3 16.8 ? ? ? ? ?? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? + ? + 20 9.3 15.3 16.2 ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + + + 21 10.4 13.5 17.3 ? ? ? ? ? ? ?? + + ? + ? + + ? + ? + + + 22 9.8 12.9 16.7 ? ? ? ? ? ? ? ? ? ? ?+ + + + ? + + + + ? + + ? + ? ? 23 10.8 14.2 17.3 ? ? ? ? ? ? ? ? ?? ? ? + ? ? + + + ? + 24 10.9 13.3 17.8 ? ? ? ? ? ? ? ? + + + + ? ++ + + + ? + + ? ? 25 10.6 — 13.8 ? ? ? ? ? ? ? ? ? ? ? 26 10.6 14.316.3 ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? + ? ? ? 27 10.5 12.9 17.4 ?? ? ? ? ? ? ? + ? + + + + ? ? ? + + ? ? + + + + 28 11.0 — 12.4 ? ?? ? ? ? 29 8.7 — 12.3 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 30 10.9 — 14.5 ?? ? ? ? ? ? ? ? ? ? ? ? 31 11.0 14.6 17.5 ? ? ? ? ? ? ? ? ? ? ? ? ++ + + + + + + + + ? + 32 10.8 14.1 17.6 ? ? ? ? ? ? ? ? ? ? ? + + ?? + ? ? ? ? ? ? 33 11.3 14.4 18.2 ? ? ? ? ? ? ? ? ? ? ? + + ? + + ?? + ? ? ? ? ? 34 11.4 13.8 18.3 ? ? ? ? ? ? ? + ? ? ? + ? ? ? + + +? ? + ? + 35 11.3 13.7 17.8 ? ? ? ? ? ? ? + + + ? + ? ? ? + + + ? ++ 36 11.2 13.5 15.7 ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? 37 11.314.5 16.3 ? ? ? ? ? ? ? ? ? ? ? + ? + + ? ? ? 38 11.2 14.3 17.2 ? ?? ? ? ? ? ? ? ? ? + ? ? + ? + + + + + + ? 39 11.6 13.9 14.7 ? ? ? ?? + ? ? ? 40 11.8 14.1 17.9 ? ? ? ? + ? + ? + ? + + + + ? ? ? ? 4111.4 13.3 18.2 ? ? ? ? + + + ? + ? ? ? ? ? + + + + + ? ? 42 11.514.0 17.9 ? ? ? ? ? ? ? + + ? ? ? ? ? ? ? + + ? + ?