Question

question 4
given a standardized normal distribution, what is the probability that z is between -1.57 and 1.84?
0.9089
0.253
0.0582

Explanation:

Step1: Find \(P(Z < 1.84)\)

Using the standard normal distribution table, \(P(Z < 1.84)=0.9671\)

Step2: Find \(P(Z < - 1.57)\)

Using the standard normal distribution table, \(P(Z < -1.57)=0.0582\)

Step3: Calculate \(P(-1.57<Z<1.84)\)

By the property \(P(a < Z < b)=P(Z < b)-P(Z < a)\), we have \(P(-1.57 < Z < 1.84)=P(Z < 1.84)-P(Z < -1.57)\)
Substitute the values: \(P(-1.57 < Z < 1.84)=0.9671 - 0.0582=0.9089\)

Answer:

0.9089