Probabilities in the standard normal distribution are found using the Z-table: (1) 0.8849, (2) 0.7580, (3) 0.6293.
To find probabilities in the standard normal distribution, we refer to the Z-table, which provides the cumulative probability up to a certain Z-score.
1. P(z < 1.2) :
Using the Z-table, we find the probability that a randomly selected value from a standard normal distribution is less than 1.2. The Z-table indicates this probability as approximately 0.8849.
2. P(z > 0.7) :
Similarly, looking up the Z-score of 0.7 in the table and subtracting it from 1 gives the probability that a value is greater than 0.7. The result is approximately 0.7580.
3. P(-0.2 < z < 1.3) :
By finding the cumulative probabilities for Z-scores of -0.2 and 1.3 and subtracting, we obtain the probability that a value falls between -0.2 and 1.3. The result is approximately 0.6293.
In summary, for the standard normal distribution:
(1) P(z < 1.2) is approximately 0.8849.
(2) P(z > 0.7) is approximately 0.7580.
(3) P(-0.2 < z < 1.3) is approximately 0.6293.