Final answer:
To calculate the probability, first find the standard error by dividing the standard deviation by the square root of the sample size, then calculate the z-score for the sample mean of 245 days, and finally use the TI-84 PLUS to find the corresponding probability through the normal distribution function.
Step-by-step explanation:
To find the probability that a random sample of 49 pregnancies has a mean gestation period of 245 days or less, given that the population mean is 249 days, and standard deviation is 12, you will need to utilize the Central Limit Theorem and the standard normal distribution.
First, calculate the standard error of the mean, which is the standard deviation of the distribution of sample means. The standard error (SE) is found by dividing the population standard deviation by the square root of the sample size (n). SE = σ / √n = 12 / √49.
Next, you will calculate the z-score for the sample mean of 245 days. The z-score is the number of standard errors that a point is away from the mean. Z = (X - μ) / SE, where X is the sample mean and μ is the population mean.
Once you have the z-score, you can use the TI-84 PLUS to find the probability corresponding to this z-value by using the normal distribution function. However, the exact steps might vary depending on your calculator's model and software version.