Final answer:
To find the probability that a comparable restaurant meal at home costs not equal to $12.80, calculate the z-score of $12.80 and use the standard normal distribution table to find the corresponding probability.
Step-by-step explanation:
To find the probability that a comparable restaurant meal at home costs not equal to $12.80, we need to calculate the z-score of $12.80 and then find the corresponding probability using the standard normal distribution table.
First, we calculate the z-score using the formula:
z = (x - mean) / standard deviation
where x is $12.80, mean is the average cost of restaurant meals at home, and standard deviation is the standard deviation of restaurant meal costs.
Using the formula, we plug in the values:
z = (12.80 - mean) / 2
To find the probability, we look up the z-score in the standard normal distribution table.
For example, if the z-score corresponds to a probability of 0.2, then the probability that a comparable restaurant meal at home costs not equal to $12.80 is 1 - 0.2 = 0.8.