3.)If the weights of 500 students are normally distributed with a mean of 40
kgs and a variance Of 16 kgs2,
a. determine the percentage of students with weights lower than 50 kgs.
b. How many students have weights exceeding 55 kgs.?
a. P(X<50)=P(Z<50−404)=P(Z<2.5)=0.9938=99.38%.P(X<50)=P(Z<\frac{50-40}{4})=P(Z<2.5)=0.9938=99.38\%.P(X<50)=P(Z<450−40)=P(Z<2.5)=0.9938=99.38%.
b. P(X>55)=P(Z>55−404)=P(Z>3.75)=0.0001.P(X>55)=P(Z>\frac{55-40}{4})=P(Z>3.75)=0.0001.P(X>55)=P(Z>455−40)=P(Z>3.75)=0.0001.
N=500∗0.0001=0.05≈0.N=500*0.0001=0.05\approx 0.N=500∗0.0001=0.05≈0.
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