Question

find the probability using the normal distribution: ( p(-1.12 < z < 2.27) ). use the standard normal distribution table and enter the answer to 4 decimal places.( p(-1.12 < z < 2.27)=)

Explanation:

Step1: Use the property of normal distribution

We know that \(P(a < z < b)=P(z < b)-P(z < a)\). Here \(a=-1.12\) and \(b = 2.27\). So \(P(-1.12<z<2.27)=P(z < 2.27)-P(z<-1.12)\)

Step2: Look up values in the standard normal table

From the standard - normal distribution table:

• For \(z = 2.27\), \(P(z < 2.27)=0.9884\)
• For \(z=-1.12\), \(P(z < - 1.12)=0.1314\)

Step3: Calculate the probability

Substitute the values into the formula: \(P(-1.12 < z < 2.27)=0.9884-0.1314\)

Answer:

\(0.8570\)