Solve the problem.
-For women aged 18-24, systolic blood pressures (in mm Hg)are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 36 women are selected at random from a population of 300 women aged 18-24, find the probability that their mean systolic blood pressure will be less than 110 mm Hg. Assume that the sampling is done without replacement and use a finite population correction factor with N = 300.

Question

Quizplus · Accepted Answer

The probability that the mean systolic blood pressure of 36 randomly selected women will be less than 110 mm Hg can be found using the formula for the standard error of the mean in a finite population, which incorporates the finite population correction factor (FPC). The FPC is calculated as sqrt((N-n)/(N-1)), where N is the population size (300) and n is the sample size (36). The standard error of the mean (SEM) is then σ/√n * FPC, where σ is the population standard deviation (13.1). The z-score for the mean of 110 mm Hg is calculated using the formula (X̄ - μ) / SEM, where X̄ is the sample mean (110) and μ is the population mean (114.8). Finally, the z-score is used to find the probability from the standard normal distribution. The calculation results in a probability that corresponds to option D, indicating a very low likelihood of the sample mean being less than 110 mm Hg.

Solve the Problem. -For Women Aged 18-24, Systolic Blood Pressures (In Mm Hg)are