statistics

The probability that an 18-year-old man is between 67 and 69 inches tall is 0.341. This can be calculated using the z-score formula to find the relative position of the data points in relation to the mean and then calculating the probability of the area within the range of 67 and 69 inches. The z-score formula is z-score=(x - mean)/standard deviation, where x is the data point we are interested in finding the probability of. In this case, we want to find the probability of an 18-year-old man being between 67 and 69 inches tall. Since the mean of 68 inches is right in the middle of the range, we can start by figuring out the z-score of 67 inches. z-score=(67-68)/3 = -0.333 To calculate the z-score for 69 inches, we can use the same formula: z-score=(69-68)/3 = 0.333 We can then use the z-table to find the two probability values at each of these z-scores. The probability of being at or to the left of -0.333 is 0.380, and the probability of being at or to the left of 0.333 is 0.721. To find the probability of being between the two values, we can subtract the two probability values: 0.721 - 0