find the indicated probability using the standard normal distribution. p(z < - 0.18 or z > 0.18) click here…
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.)
Answer
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)