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Given that x is a normal variable with mean μ = 49 and standard deviation σ = 6.7, find the following probabilities. (Round your answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c) P(50 ≤ x ≤ 60)

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altavistard

Answer:

0.9500, 0.4407, 0.3904

Step-by-step explanation:

(a) P(x ≤ 60).  We need to find the area under the standard normal curve to the left of x = 60.  The appropriate command when using a TI-83 Plus calculator with statistical functions is normcdf(-1000, 60, 49, 6.7).  This comes out to 0.9500.  P(x ≤ 60) = 0.9500

(b) P(x ≥ 50) would be normcdf(50, 1000,49, 6.7), or 0.4407

(c) P(50 ≤ x ≤ 60) would be normcdf(50,60,49,6.70, or 0.3904

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