Arandom sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. the probability that the sample mean is between 15 and 18 is 0.8641 0.8185 0.8413 0.0228

N = 36, the sample size
μ = 17, the population mean
σ = 6, the population standard deviation

When the random variable is x = 15, obtain
z = (x - μ)/(σ/√n) = (15 - 17)/1 = -2
From standard tables,
P(x <15) = 0.0228

Similarly, when x = 18, obtain
z = (18 - 17)/1 = 1
P(x <18) = 0.8413

Therefore
P(15 < x < 18) = 0.8413 - 0.0228 = 0.8185

0.8185

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