Question

Suppose cattle in a large herd have a mean weight of 1228lbs and a variance of 8100. What is the probability that the mean weight of the sample of cows would be greater than 1240lbs if 115 cows are sampled at random from the herd? Round your answer to four decimal places.

Answer 1

To find the probability that the mean weight of the sample of cows would be greater than 1240lbs, use the Central Limit Theorem and properties of a normal distribution.

Step-by-step explanation:

To find the probability that the mean weight of the sample of cows would be greater than 1240lbs, we can use the Central Limit Theorem and the properties of a normal distribution.

1. Calculate the standard deviation of the sample mean, which is the population standard deviation divided by the square root of the sample size: 15 / sqrt(115) ≈ 1.3981.
2. Standardize the value 1240 using the sample mean and the standard deviation of the sample mean: (1240 - 1228) / 1.3981 ≈ 0.8588.
3. Find the probability that a standardized value is greater than 0.8588 using a standard normal distribution table or a calculator: P(Z > 0.8588) ≈ 0.1956.

The probability that the mean weight of the sample of cows would be greater than 1240lbs is approximately 0.1956.