Question

find the indicated probability using the standard normal distribution. p(-1.38 < z < 1.38) click here to view page 1 of the standard normal table. click here to view page 2 of the standard normal table. p(-1.38 < z < 1.38)= (round to four decimal places as needed.)

Explanation:

Step1: Use property of standard - normal

$P(-1.38 < z < 1.38)=P(z < 1.38)-P(z < - 1.38)$

Step2: Use symmetry of standard - normal

Since the standard - normal distribution is symmetric about $z = 0$, $P(z < -1.38)=1 - P(z < 1.38)$. So $P(-1.38 < z < 1.38)=P(z < 1.38)-(1 - P(z < 1.38)) = 2P(z < 1.38)-1$.

Step3: Look up in standard - normal table

From the standard - normal table, $P(z < 1.38)=0.9162$.

Step4: Calculate the result

$P(-1.38 < z < 1.38)=2\times0.9162-1=1.8324 - 1=0.8324$

Answer:

$0.8324$