Assume that the random variable X is normally distributed, with mean μ = 50 and standard deviation σ = 16.Compute the probability P(6

Question

Assume that the random variable X is normally distributed, with mean μ = 50 and standard deviation σ = 16.Compute the probability P(6 < X < 70).
A) 0.8914
B) 0.8819
C) 0.8944
D) 0.7888

Quizplus · Accepted Answer

To find P(6 < X < 70) for a normally distributed variable X with mean μ = 50 and standard deviation σ = 16, we use the Z-score formula: Z = (X - μ) / σ. For X = 6, Z = (6 - 50) / 16 = -2.75. For X = 70, Z = (70 - 50) / 16 = 1.25. Using standard normal distribution tables or a calculator, we find P(Z < 1.25) and P(Z < -2.75), then subtract the latter from the former to get the probability between these Z-scores. The closest value to the result from standard Z-tables or calculators is 0.8914.

Assume That the Random Variable X Is Normally Distributed, with Mean