Question

The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 1100lbs. Find the probability that the weight of a randomly selected steer is greater than 920lbs. Round your answer to four decimal places.

Answer 1

Answer: 0.7257

Step-by-step explanation:

Given : The weights of steers in a herd are distributed normally.

$\mu= 1100\text{ lbs }$

Standard deviation : $\sigma=300 \text{ lbs }$

Let x be the weight of the randomly selected steer .

Z-score : $\dfrac{x-\mu}{\sigma}$

$z=\dfrac{920-1100}{300}=-0.6$

The the probability that the weight of a randomly selected steer is greater than 920 lbs using standardized normal distribution table  :

$P(x>920)=P(z>-0.6)=1-P(z$    

Hence, the probability that the weight of a randomly selected steer is greater than 920lbs =0.7257