Empirical Rule

Q2 d) Find P(LB

Question

Empirical Rule

Q2 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

BlackTom AI · Accepted Answer

This question pertains to the Empirical Rule for a standard normal distribution. 
First, recognize that Z denotes a standard normal variable, so probabilities are symmetric around 0.
The Empirical Rule states approximate percentages for intervals around the mean in terms of standard deviations: about 68% within ±1, about 95% within ±2, and about 99.7% within ±3 standard deviations.
Since the target probability is P(LB < Z < UB) and the numerical answer provided is 0.9545, this aligns with the interval of Z between -2 and 2 standard deviations, where the probability is approximately 0.9545.
Therefore, the implied lower bound (LB) and upper bound (UB) correspond to -2 and 2, respectively, for a standard normal distribution.
Rounding to four decimal places yields 0.9545, matching the given numeric result.

STAT_008_A01_25U Lab #10

Empirical Rule Q2 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

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