Final answer:
To estimate the probability that Xbar (the sample average) is higher than 76 grams OR smaller than 69 grams, use the Central Limit Theorem and calculate the z-scores for both values. Then use the z-scores to find the probabilities from the standard normal distribution table and add them together.
Step-by-step explanation:
To estimate the probability that Xbar (the sample average) is higher than 76 grams OR smaller than 69 grams, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases. Since the sample size is 8, we can assume that the sampling distribution of Xbar is approximately normal.
To find the probability, we need to calculate the z-scores for 76 grams and 69 grams, and then use the z-scores to find the probabilities from the standard normal distribution table.
First, calculate the z-score for 76 grams:
z = (76 - 72) / (5 / sqrt(8))
= 2.829
The probability that Xbar is higher than 76 grams can be found by looking up the area under the normal curve to the right of 2.829.
The z-score for 69 grams can be calculated using the same formula:
z = (69 - 72) / (5 / sqrt(8))
= -2.121
The probability that Xbar is smaller than 69 grams can be found by looking up the area under the normal curve to the left of -2.121.
Add these two probabilities to estimate the probability that Xbar is higher than 76 grams OR smaller than 69 grams.