A variable of a population is normally distributed with mean μ and standard deviation σ. For samples of size n, complete parts (a) through (d) below. a. Approximately 68% of all possible samples have means that lie within ! of the population mean, . Justify your answer. Since the var able is no maly distributed its sample mean ▼ noma ydistributed with mean and standard deviation according to he central approximately 68% of al possible observations from a normal distribution lie within standard deviation(s) of the population mean, μ. b. Approximately 95% of all possible samples have means that lie within | | of the population mean, p. Justify your answer mitteo em Using the empina rule for vanables approximately 95% of al possible observations from a normal distribution lie thin standard dev ation s of the population mean . c Approximately 99.7% of all possible samples have means that lie within of the population mean, p. Justify your answer. Since the variable s norma y distributed its sam e mean x ▼ norma y distributed with mean ▼ and standard deviation ▼ accordin to he entra imit the rem. sin teempirical 1 or approximately 99 7% of all possible observations from a normal distribution lie within standard deviations of the population mean, p. d. 100(1-α)% of all possible samples have means that lie within Justify your answer. Since the variable is normally distributed, its sample mean x ▼ normally distributed. Using the empirical rule or variables, 100 1-α)% of all possible observations from a normal distribution lie within a abies Vof the population mean, u. ▼ standard deviation(s) of the population mean, I.
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