Question

find the indicated probability using the standard normal distribution. p(z < - 0.18 or z > 0.18) click here to view page 1 of the standard normal table. click here to view page 2 of the standard normal table. p(z < - 0.18 or z > 0.18)= (round to four decimal places as needed.)

Explanation:

Step1: Use symmetry of standard normal

The standard - normal distribution is symmetric about \(z = 0\). So \(P(z<-0.18)=P(z > 0.18)\). Also, the total area under the standard - normal curve is 1, and \(P(-0.18\leq z\leq0.18)+P(z < - 0.18)+P(z>0.18)=1\).

Step2: Find \(P(z < - 0.18)\) from table

Looking up \(z=-0.18\) in the standard - normal table, we find \(P(z < - 0.18)\). The standard - normal table gives the area to the left of \(z\). From the table, \(P(z < - 0.18)=0.4286\).

Step3: Calculate the required probability

Since \(P(z < - 0.18)=P(z > 0.18)\), then \(P(z < - 0.18\text{ or }z > 0.18)=2P(z < - 0.18)\). Substituting the value of \(P(z < - 0.18)\) we found in Step 2, we get \(2\times0.4286 = 0.8572\).

Answer:

\(0.8572\)