6-1 The Standard Normal Distribution 259 15. z 0 0.9265 16. z 0 0.2061 Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers to four decimal places. 17. Less than -2.00 18. Less than -0.50 19. Less than 1.33 20. Less than 2.33 21. Greater than 1.00 22. Greater than 2.33 23. Greater than -1.75 24. Greater than -2.09 25. Between 1.50 and 2.00 26. Between 1.37 and 2.25 27. Between -1.22 and -2.36 28. Between -0.45 and -2.08 29. Between -1.55 and 1.55 30. Between -0.77 and 1.42 31. Between -2.00 and 3.50 32. Between -3.52 and 2.53 33. Greater than -3.77 34. Less than -3.93 35. Between -4.00 and 4.00 36. Between -3.67 and 4.25 Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the bone density test score corresponding to the given information. Round results to two decimal places. 37. Find P99, the 99th percentile. This is the bone density score separating the bottom 99% from the top 1%. 38. Find P15, the 15th percentile. This is the bone density score separating the bottom 15% from the top 85%. 39. If bone density scores in the bottom 1% and the top 1% are used as cutoff points for levels that are too low or too high, find the two readings that are cutoff values. 40. Find the bone density scores that are the quartiles Q1, Q2, and Q3. Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places. 41. z0.25 42. z0.90 43. z0.02 44. z0.05 Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2. 45. About % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean).
RkJQdWJsaXNoZXIy NjM5ODQ=