Answer to Question #111277 in Statistics and Probability for dorothy

Question

The weight of 500 college students is 70 kg and the standard deviation is 3 kg. Assuming that the weight is normally distributed, determine how many students weigh: between 60 kg and 75 kg, more than 90 kg, less than 64 kg, exactly 64 kg

Answer 1

1) Between 60 kg and 75 kg:

P(60<x<75)=P((60-70)/3)<Z<((75-70)/3))=P(-3.33<Z<1.67)=P(Z <1.67)-(1-P(Z<3.33))=0.9525-(1-0.9996)=0.9521 => N=500*0.9521=476

2)more than 90 kg:

P(x>90)=P(Z>((90-70)/3))=P(Z>6.67)=1-P(Z<6.67)=1-1=0

N=0

3)Less than 64 kg:

P(X<64)=P(Z<((64-70)/3))=P(Z<-2)=1-p(Z<2)=1-0.97725=0.02275

N=500*0.0227=11

4)Exactly 64 kg:

P(X=64)=P(Z=((64-70)/3))=p(Z=-2)=0

N=0