Question #341620

If the weights of 600 students are normally distributed with mean of 50 kilograms and a variance of 16kilograms.



a.) Determine the percentage of students with weights lower than 55 kgs.



b.) How many students with weight between 50kgs and 55kgs.

1
Expert's answer
2022-05-16T23:36:45-0400

Let X=X= the weight of student: XN(μ,σ2).X\sim N(\mu, \sigma^2).

Given μ=50kg,σ=16kg\mu=50kg, \sigma=\sqrt{16}kg

a)


P(X<55)=P(Z<555016)P(X<55)=P(Z<\dfrac{55-50}{\sqrt{16}})

=P(Z<1.25)=0.89435=P(Z<1.25)=0.89435

0.89435(600)=5370.89435(600)=537

537 students


b)


P(50<X<55)=P(Z<555016)P(50<X<55)=P(Z<\dfrac{55-50}{\sqrt{16}})

P(Z505016)=P(Z<1.25)P(Z0)-P(Z\le\dfrac{50-50}{\sqrt{16}})=P(Z<1.25)-P(Z\le 0)

=0.894350.5=0.39435=0.89435-0.5=0.39435

0.39435(600)=2370.39435(600)=237

237 students



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