Explanation:
(a) To find the z-score for a weight of 210 pounds, we need to calculate how many standard deviations away from the mean this weight is. The formula for z-score is z = (x - mean) / standard deviation, where x is the given weight. Using the formula, we can calculate: z = (210-172)/27 Simplifying the calculation: z = 38/27 Rounding the answer to 2 decimal places: z = 1.41 Therefore, the z-score for a weight of 210 pounds is approximately 1.41. (b) To find the z-score for a weight of 148 pounds, we can use the same formula: z = (148-172) / 27 Calculating: z = -24 / 27 Rounding to 2 decimal places: z =-0.89 So, the z-score for a weight of 148 pounds is approximately -0.89. (c) For a weight of 148 pounds is approximately -0.89. (c) For a weight of 170 pounds: z = (170 - 172)/27 Simplifying: z = -2/27 Rounding to 2 decimal places: z = -0.07 Hence, the z-score for a weight of 170 pounds is approximately -0.07. (d) Finally, for a weight of 233 pounds: z = (233-172)/27 Calculating: z = 61/27 Rounding to 2 decimal places: z = 2.26 Thus, the z-score for a weight of 233 pounds is approximately 2.26. Hope this helps