Question

The weights of stairs in a herd are distributed normally the standard deviation is 200 pounds in a mean steer weight is 1000 pounds find the probability that the weight of a randomly selected steer is between 1117 and 1279 pounds round your answer to four decimals

Answer 1

Hi,

0.1963 (I am using table with 4 decimals)

Explanation:

`z=(x-\mu)/(\sigma) =(x-1000)/(200) \\\\if\ x=1117\ then\ z=(1117-1000)/(200)=0.585\\\\p(z < 0.58)=0.7190\\p(z < 0.59)=0.7224\\\Longrightarrow\ p(z < 0585)=0.7207\ (\delta=0.01,\ \Delta=0.0034)\\p(x < 1117)=p(z < 0.585)=0.7207\\\\\\if\ x=1279\ then\ z=(1279-1000)/(200)=1.385\\\\p(z < 1.38)=0.9162\\p(z < 1.39)=0.9177\\\Longrightarrow\ p(z < 1.385)=0.91695\ (\delta=0.01,\ \Delta=0.00075)\\p(x < 1279)=p(z < 1.385)=0.91695\\\\`

`Thus\\\\p(1279 < x < 1279)=p(0586 < z < 1.385)\\\\=0.91695-0.7207=0.19625\\\\\approx{\boxed{0.1963}}`