Question

Suppose that the mean systolic blood pressure for women over age seventy is 134 mmHg (millimeters of mercury), with a standard deviation of 7 mmHg
Suppose that the blood pressures are normally distributed. Complete the following statements.
(a) Approximately 99.7% of women over seventy have blood pressures between mmHg
and mmHg
(b) Approximately 2 v of women over seventy have blood pressures between 127
mmHg and 141 mmHg.

Answer 1

Answer:

See below for answers (in bold) and explanations

Step-by-step explanation:

Part A

According to the Empirical Rule, 99.7% of the data in a normal distribution are ±3σ standard deviations away from the mean. Hence, approximately 99.7% of women over seventy have blood pressures between 134-3σ = 134-3(7) = 134-21 = 113 mmHg and 134+3σ = 134+3(7) = 134+21 = 155 mmHg.

Part B

As 141-134=134-127=7, this represents ±1σ standard deviations away from the mean of 134 mmHg, which corresponds to 68% of the data by the Empirical Rule. Hence, approximately 68% of women over seventy have blood pressures between 127 mmHg and 141 mmHg