Question

question 3
find ( p(zgeq - 0.57)=)_________

Explanation:

Step1: Use the property of the standard normal distribution

We know that \(P(Z\geq a)=1 - P(Z < a)\) for any real number \(a\). Here \(a=- 0.57\), so \(P(Z\geq - 0.57)=1 - P(Z < - 0.57)\)

Step2: Use the symmetry of the standard normal distribution

The standard normal distribution \(Z\sim N(0,1)\) is symmetric about \(z = 0\), i.e., \(P(Z < -x)=1 - P(Z < x)\). Also, we can use the standard - normal table (or z - table). Looking up the value of \(P(Z < - 0.57)\) in the standard - normal table. The value of \(P(Z < -0.57)\) is \(0.2843\)

Step3: Calculate the probability

Substitute the value of \(P(Z < -0.57)\) into the formula from Step1. \(P(Z\geq - 0.57)=1-0.2843 = 0.7157\)

Answer:

\(0.7157\)