the probability that the weight of a randomly selected steer is between 1020 and 1709 lbs, we need to use the normal distribution formula to calculate the area under the curve for this range of weights.
The normal distribution formula is:
f(x) = (1 / (sigma * sqrt(2 * pi))) * e^(-1/2 * ((x - mu) / sigma)^2)
Where f(x) is the probability density function, sigma is the standard deviation, mu is the mean, and pi is approximately 3.14159.
We can use this formula to calculate the probability that the weight of a randomly selected steer is between 1020 and 1709 lbs. The probability is equal to the area under the curve for this range of weights, which can be calculated as follows:
P = integral from 1020 to 1709 of f(x) dx
Plugging in the values for sigma and mu, we get:
P = integral from 1020 to 1709 of (1 / (300 * sqrt(2 * pi))) * e^(-1/2 * ((x - 1200) / 300)^2) dx
This integral can be solved using numerical integration techniques, which will give us the probability that the weight of a randomly selected steer is between 1020 and 1709 lbs.
The probability is approximately 0.6174, which when rounded to four decimal places is 0.6174.