Final answer:
To find the minimum red blood cell count in the top 27% and the maximum count in the bottom 16%, first calculate the corresponding z-scores using the formula z = (x - mean) / std. Then, use the formula x = z * std + mean to find the counts. The minimum count is approximately 5.51 million cells per microliter and the maximum count is approximately 5.26 million cells per microliter.
Step-by-step explanation:
To find the minimum red blood cell count that can be in the top 27% of counts, we need to find the z-score corresponding to this percentile and use it to calculate the count. The z-score can be calculated using the formula z = (x - mean) / std, where x is the given percentile and std is the standard deviation. Substituting the given values, we have z = (27 - 50) / 27 = -0.5556. Using a z-table, we find that the corresponding z-value is approximately -0.5556. Now we can use the formula x = z * std + mean to find the minimum count. Substituting the values, we get x = -0.5556 * 0.4 + 5.7 = 5.5102. Therefore, the minimum red blood cell count in the top 27% is approximately 5.51 million cells per microliter.
To find the maximum red blood cell count that can be in the bottom 16% of counts, we can follow a similar process. The z-score corresponding to the 16th percentile is z = (16 - 50) / 27 = -1.1852. Using a z-table, we find that the corresponding z-value is approximately -1.1852. Using the formula x = z * std + mean, we can find the maximum count. Substituting the values, we get x = -1.1852 * 0.4 + 5.7 = 5.2612. Therefore, the maximum red blood cell count in the bottom 16% is approximately 5.26 million cells per microliter.