Question

A livestock company reports that the mean weight of a group of young steers is 1148 pounds with a standard deviation of 64 pounds. Based on the model ​N(1148,64​) for the weights of​ steers, what percent of steers weigh ​

a) over 1300 ​pounds?

​b) under 1200 ​pounds?

​c) between 1000 and 1250 ​pounds?

Answer 1

a)P( X>1300) = 1 - P(X<1300) = ?
  
I know that, z = (X-mean)/(sd)  
z1 = (1300-1148)/64) =   2.3750
  
hence,  
P( X>1300) = 1- P(Z<2.375)
P( X>1300) = 1 - NORMSDIST(2.375)
P( X>1300) = 0.008774

b)
P( X<1200) = ?
  
I know that, z = (X-mean)/(sd)  
z1 = (1200-1148)/64)   0.8125
hence,  
P( X<1200) = P(Z<0.8125)
P( X<1200) = NORMSDIST(0.8125)
P( X<1200) = 0.7917
  
c)
P(1000 < X < 1250) = P(X<1250) - P(X<1000) = ?
  
I know that, z = (X-mean)/(sd)  
z1 = (1000-1148)/64) =   -2.3125
z2 = (1250-1148)/64) =   1.5938
  
hence,  
P(1000 < X < 1250) = P(Z<1.5938) - P(Z<-2.3125)
P(1000 < X < 1250) = NORMSDIST(1.5938) - NORMSDIST(-2.3125)
P(1000 < X < 1250) = 0.9341