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A normal distribution has mean 50 and variance 9. Find the probability that

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A normal distribution has mean 50 and variance 9. Find the probability that

(i) The value of normal variable X lies between 50 and 53.

(ii) The value of normal variable X lies between 47 and 53.

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Here, µ = 50; σ2 = 9

∴ σ = 3

∴ P [47 ≤ X ≤ 53] = P [- 1≤ Z ≤ 1]

= 2P[0 ≤ Z ≤ 1]
= 2 [0.3413]
= 0.6826

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