Find P(-1.88 < z < 2.11). Give correct answer to four decimal places.

Answer 1

This problem is asking for the probability a z-score will be in a certain range. Here are two ways to solve it, use whichever makes more sense to you.

Method A finds the probability a z-score will be outside the range and subtracts that from 100%:

1) find the probability the z score is below the range, P(z<-1.88) = 0.030054 which is 3.0054%

2) find the probability the z score is above the range, P(z>2.11) = 0.017429 which is 1.7429%

3) subtract those probabilities from 100%, 100% - 3.0054% - 1.7429% = 95.2517%.

P(-1.88 < z < 2.11) = 95.2517%.

This method finds the probability a z-score will be below the maximum of the range, then subtracts the probability the z score is below the minimum of the range:

1) find the probability a z score is below the maximum value for the range, P(z<2.11) = .982571 which is 98.2571%

2) find the probability a z-score is below the minimum value of the range, P(z<-1..88) = .030054 which is 3.0054%

3) subtract the probability the z-score will be below the minimum of the range from the probability it will be below the maximum of the range, 98.2571% - 3.0054% = 95.2517%

P(-1.88 < z < 2.11) = 95.2517%.