Question

12. The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.4 and a standard

deviation of 62.3. (All units are 1000 cellsfuL) Using the empirical rule, find each approximate percentage below.

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?

b. What is the approximate percentage of women with platelet counts between 128.8 and 378.0?

a. Approximately

% of women in this group have platelet counts within 1 standard deviation of the mean,

or between 191.1 and 315.7.

(Type an integer or a decimal. Do not round.)

b. Approximately

% of women in this group have platelet counts between 128.8 and 378.0.

(Type an integer or a decimal. Do not round.)

Answer 1

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%

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%