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

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