Final answer:
To find the probability, standardize the values using Z = (X - µ) / σ, where X is the value, µ is the mean, and σ is the standard deviation. Calculate the Z-scores for the lower and upper values, then use the standard normal distribution table to find the probabilities. The probability that the weight of a randomly selected steer is between 1379 and 1590 pounds is approximately 0.0.
Step-by-step explanation:
To find the probability that the weight of a randomly selected steer is between 1379 and 1590 pounds, we need to standardize the values using the formula Z = (X - µ) / σ, where X is the value, µ is the mean, and σ is the standard deviation. We can then use the standard normal distribution table to find the probability. In this case, the mean (µ) is 1200 pounds and the variance (σ^2) is 90,000, so the standard deviation (σ) is √90,000 = 300 pounds.
For the lower value of 1379 pounds:
Z1 = (1379 - 1200) / 300 = 5.97 (approx)
For the upper value of 1590 pounds:
Z2 = (1590 - 1200) / 300 = 13.33 (approx)
Using the standard normal distribution table, we can find the probability for Z1 and Z2:
Probability for Z1 = 1.0 (since Z1 is larger than the highest value in the table)
Probability for Z2 = 1.0 (since Z2 is larger than the highest value in the table)
Therefore, the probability that the weight of a randomly selected steer is between 1379 and 1590 pounds is approximately 1.0 - 1.0 = 0.0.