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X is normally distributed with mean μ=100 and σ=16. Find P(98≤X<106).

X is normally distributed with mean μ=100 and σ=16. Find P(98≤X<106).

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Answer #1

X is normally distributed with a mean  μ = 100 and  σ =16  

Z = (X - μ)/σ   N(0,1)

P(98 < X <106) = P[(98 - 100/16)<(X - μ)/σ < (106 -100/100)]

  = P(-2/16/ < Z< 6/16)

= P(- 0.125 < Z < 0.375)

= P(Z < 0.375) - P(Z < - 0.125)

= P(Z < 0.375) - P(Z > 0.125)

= P(Z < 0.375) - [1 - P(Z < 0.125)]

= P(Z < 0.375) - 1 + P(Z < 0.125)

= 0.64617 - 1 + 0.54974

  = 1.19591 - 1

= 0.19591

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