Question

a. p(z > +2.00)
b. p(z > -1.00)

Explanation:

1. Recall the properties of the standard - normal distribution:

• The standard - normal distribution \(Z\sim N(0,1)\) has a cumulative - distribution function \(\varPhi(z)=P(Z\leq z)\), and the total area under the standard - normal curve is 1, i.e., \(P(Z\leq z)+P(Z > z)=1\).
• We can use the standard - normal table (z - table) to find the values of \(\varPhi(z)\).

Step 1: Calculate \(P(Z > 2.00)\)

• We know that \(P(Z > 2.00)=1 - P(Z\leq2.00)\).
• Looking up the value of \(P(Z\leq2.00)\) in the standard - normal table, we find that \(\varPhi(2.00) = 0.9772\).
• So, \(P(Z > 2.00)=1 - 0.9772=0.0228\).

Step 2: Calculate \(P(Z > - 1.00)\)

• We know that \(P(Z > - 1.00)=1 - P(Z\leq - 1.00)\).
• Since the standard - normal distribution is symmetric about \(z = 0\), \(P(Z\leq - 1.00)=1 - P(Z\leq1.00)\). Looking up the value of \(P(Z\leq1.00)\) in the standard - normal table, we find that \(\varPhi(1.00)=0.8413\). So, \(P(Z\leq - 1.00)=1 - 0.8413 = 0.1587\).
• Then \(P(Z > - 1.00)=1-0.1587 = 0.8413\).

Answer:

a. \(0.0228\)
b. \(0.8413\)