Determine the probability that a sample of 49 boxes will have a mean weight below 365grams. past records show that the population mean is 368 grams and the population standard deviation is 7. the probability will be between

To determine the probability that a sample of 49 boxes will have a mean weight below 365 grams, we can use the Central Limit Theorem and the standard normal distribution.

Step 1: Calculate the standard error of the mean (SE):

SE = population standard deviation / square root of sample size
SE = 7 / √49
SE = 7 / 7
SE = 1

Step 2: Calculate the z-score:

z = (sample mean - population mean) / SE
z = (365 - 368) / 1
z = -3

Step 3: Look up the z-score in the z-table or use a calculator to find the corresponding cumulative probability. In this case, we want to find the probability of getting a z-score less than -3.

According to the standard normal distribution table, the probability of getting a z-score less than -3 is significantly close to 0.

Therefore, the probability that a sample of 49 boxes will have a mean weight below 365 grams is very close to 0.