Final answer:
To find the values of b, d, and e in a standard normal distribution, we can use a z-table or calculator. For P(z > b) = 0.9772, we find b to be approximately 1.96. For P(-d < z < 0) = 0.025, we find d to be approximately 1.96. For P(-e < z) = 0.05, we find e to be approximately 1.645.
Step-by-step explanation:
In this question, we are given that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.
A) To find the value of b for which P(z > b) = 0.9772, we can use the standard normal distribution table or calculator. We look up the z-score that corresponds to 0.9772, which gives us a z-score of approximately 1.96. Therefore, b = 1.96.
B) To find the value of d for which P(-d < z < 0) = 0.025, we can use the standard normal distribution table or calculator. We look up the z-score that corresponds to 0.025/2 = 0.0125 (divided by 2 because we need the area in the tails). This gives us a z-score of approximately -1.96. Therefore, d = 1.96.
C) To find the value of e for which P(-e < z) = 0.05, we can use the standard normal distribution table or calculator. We look up the z-score that corresponds to 0.05, which gives us a z-score of approximately -1.645. Therefore, e = 1.645.