which of the following statements is equivalent to p(z < -2.1)?\np(z > -2.1)\n1 - p(z < 2.1)\np(z < 2.1)\n1…

which of the following statements is equivalent to p(z < -2.1)?\np(z > -2.1)\n1 - p(z < 2.1)\np(z < 2.1)\n1 - p(z > 2.1)

which of the following statements is equivalent to p(z < -2.1)?\np(z > -2.1)\n1 - p(z < 2.1)\np(z < 2.1)\n1 - p(z > 2.1)

Answer

Answer:

1 - P(z < 2.1)

Explanation:

Step1: Recall normal - distribution property

The standard normal distribution is symmetric about z = 0. The total area under the standard - normal curve is 1.

Step2: Analyze the relationship

We know that P(z < - 2.1)+P( - 2.1≤z≤2.1)+P(z > 2.1)=1. Also, due to symmetry, P(z < - 2.1)=P(z > 2.1). And P(z < 2.1)=P(z < - 2.1)+P( - 2.1≤z≤2.1). So, P(z < - 2.1)=1 - P(z < 2.1).