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.
Accepted Solution
A:
Answer: 0.7257Step-by-step explanation:Given : The weights of steers in a herd are distributed normally.[tex]\mu= 1100\text{ lbs }[/tex] Standard deviation : [tex]\sigma=300 \text{ lbs }[/tex]Let x be the weight of the randomly selected steer .Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex][tex]z=\dfrac{920-1100}{300}=-0.6[/tex]The the probability that the weight of a randomly selected steer is greater than 920 lbs using standardized normal distribution table :[tex]P(x>920)=P(z>-0.6)=1-P(z<-0.6)\\\\=1-0.2742531=0.7257469\approx0.7257[/tex] Hence, the probability that the weight of a randomly selected steer is greater than 920lbs =0.7257