The weights of steers in a herd are distributed normally The

The weights of steers in a herd are distributed normally. The standard deviation is 200 lbs and the mean steer weight is 1300 lbs. Find the probability that the weight of a randomly selected steer is between 1600 and 1740 lbs.

Please round your answer to four decimal places. Also, please show your work.

Thank you!

Solution

So the probability that the weight of a randomly selected steer is between 1600 and 1740 lbs is

P(1600<X<1740) = P((1600-1300)/200 <(X-mean)/s <(1740-1300)/200)

=P(1.5<Z<2.2) =0.0529 (from standard normal table)