Answer:
a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or
between 191.1 and 315.7?
68%
b. What is the approximate percentage of women with platelet counts between 128.8 and 378.0?
95%
Step-by-step explanation:
The Empirical rule formula states that:
1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or
between 191.1 and 315.7?
μ = mean = 253.4
σ = standard deviation = 62.3.
μ - σ
= 253.4 - 62.3
= 191.1
μ + σ
= 253.4 + 62.3
= 315.7
Therefore, the first empirical rule holds for Question a. This states that 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
Therefore, the approximate percentage of women with platelet counts between 191.1 and 315.7 is 68%
b. What is the approximate percentage of women with platelet counts between 128.8 and 378.0?
μ = mean = 253.4
σ = standard deviation = 62.3.
Applying the second rule of the empirical rule: this states that: 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
For x = 128.8
μ - 2σ
= 253.4 - 2 × 62.3
= 128.8
μ + 2σ
= 253.4 + 2 × 62.3
= 378
Therefore, the approximate percentage of women with platelet counts between 128.8 and 378.0 is 95%
