M = 1200
σ = 102
a. P(less than 1000 servings) = P(X < 1000)
=P(σX−M<σ1000−M)
=P(Z<1021000−1200)
=P(Z<−1.96)=0.025
b. P(more than 1400 servings) = P(X>1400)
=P(σX−M>σ1400−M)
=P(Z>1021400−1200)
= P(Z > 1.96)
= 1 – P(Z ≤ 1.96) = 1 – 0.975 = 0.025
c. P(between 1100 to 1300 serving) = P(1100 < X < 1300)
=P(σ1100–M<σX–M<σ1300–M)
=P(1021100–1200<Z<1021300–1200)
= P(-0.98 < Z < 0.98)
=P(Z ≤ 0.98) – P(Z ≤ -0.98) = 0.8365 – 0.1635 = 0.673
d. P(less than 1000 but not less than 1350) = P(1000 > X) + P(X> 1350)
=P(σ1000–M>σX–M)+P(σX–M>σ1350–M)
=P(1021000–1200>Z)+P(Z>1021350–1200)
= P(-1.96 > Z) + P(Z > 1.47)
= P(Z < -1.96) + (1 – P(Z ≤ 1.47)) = 0.025 + (1 – 0.9292) = 0.0958
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