Final answer:
The probability of a woman's systolic blood pressure exceeding 120 mm Hg can be calculated using the mean and standard deviation of the normal distribution of blood pressure. For individual cases, the z-score can be used to determine the number of standard deviations above the mean, while for a group, the central limit theorem helps calculate the mean probability. Normal blood pressure classifications are essential to assess and manage cardiovascular health risks.
Step-by-step explanation:
To calculate the probability that a woman's systolic blood pressure is greater than 120 mm Hg, you need to consider the population distribution for systolic blood pressure. If systolic blood pressure follows a normal distribution, as suggested by the information given about Kyle's z-score, you can utilize the mean (μ = 125 mm Hg) and standard deviation (σ = 14 mm Hg) to calculate this probability.
Assuming a normal distribution, you can use z-scores to determine the probability of a randomly selected woman from this population having a systolic blood pressure greater than 120 mm Hg. A z-score represents the number of standard deviations a data point is from the mean. For example, Kyle's z-score of 1.75 indicates that his systolic blood pressure is 1.75 standard deviations above the mean.
To calculate the probability for a single systolic blood pressure reading above 120 mm Hg, you can use standard statistical tables or a calculator, comparing the z-score corresponding to 120 mm Hg using the given mean and standard deviation. For a group of 40 women, the central limit theorem would apply, and you'd look at the sampling distribution of the mean, which has its own mean (μ) and standard deviation (σ/√40).