The random variable X is normally distributed with mean 82 and standard deviation 7.4. Find the value of q such that P (82 - q < X < 82 + q) = 0.44.

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Deanna Holland

Mathematics

4 May, 18:03

The random variable X is normally distributed with mean 82 and standard deviation 7.4. Find the value of q such that P (82 - q < X < 82 + q) = 0.44.

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Colton · Answer 1

P (82 - q < x < 82 + q) = 0.44

P (x < 82 + q) - P (82 - q) = 0.44

P (z < (82 + q - 82) / 7.4 - P (z < (82 - q - 82) / 7.4) = 0.44

P (z < q/7.4) - P (z < - q/7.4) = 0.44

P (z < q/7.4) - (1 - P (z < q/7.4) = 0.44

P (z < q/7.4) - 1 + P (z < q/7.4) = 0.44

2P (z < q/7.4) - 1 = 0.44

2P (z < q/7.4) = 1.44

P (z < q/7.4) = 0.72

P (z < q/7.4) = P (z < 0.583)

q/7.4 = 0.583

q = 0.583 x 7.4 = 4.31