which of the following statements is equivalent to $p(z\\geq1.7)$?\n$p(z\\geq - 1.7)$\n$1 - p(z\\geq…

which of the following statements is equivalent to $p(z\\geq1.7)$?\n$p(z\\geq - 1.7)$\n$1 - p(z\\geq - 1.7)$\n$p(z\\leq1.7)$\n$1 - p(z\\geq1.7)$

which of the following statements is equivalent to $p(z\\geq1.7)$?\n$p(z\\geq - 1.7)$\n$1 - p(z\\geq - 1.7)$\n$p(z\\leq1.7)$\n$1 - p(z\\geq1.7)$

Answer

Answer:

1 - P(z < 1.7)

Explanation:

Step1: Recall total probability rule

The total area under the standard - normal curve is 1. That is, (P(Z<\infty)=1).

Step2: Express (P(z\geq1.7)) in terms of (P(z < 1.7))

We know that (P(Z < 1.7)+P(Z\geq1.7)=1).

Step3: Solve for (P(z\geq1.7))

By rearranging the equation (P(Z < 1.7)+P(Z\geq1.7)=1), we get (P(Z\geq1.7)=1 - P(Z < 1.7)). Since the given options do not have (P(z < 1.7)) directly, and we know that (P(z\geq - 1.7)\neq P(z\geq1.7)), (1 - P(z\geq - 1.7)\neq P(z\geq1.7)), (P(z\leq1.7)\neq P(z\geq1.7)), and (1 - P(z\geq1.7)\neq P(z\geq1.7)). The correct equivalent statement for (P(z\geq1.7)) is (1 - P(z < 1.7)) among the concepts related to normal - distribution probabilities.