The Scholastic Assessment Test (SAT) is standardized to have a population mean = 500 and a

The Scholastic Assessment Test (SAT) is standardized to have a population mean μ = 500 and a population standard deviation σ = 100. Suppose that a researcher gives the SAT to a random sample of 50 males and 50 females, yielding sample means of 511 and 541, respectively. Based on these samples’ sizes, the researcher has already calculated the true standard deviation of the sampling distribution of the difference between means (σx₁-X₂) to be 20. Based on the areas under the normal curve given in Table A, find the probability of obtaining a sample mean for females that is at least 30 points higher than the sample mean for males.