Final answer:
To find the probability that X is between 38 and 76, we can calculate the z-scores for these values and use a standard normal distribution table or calculator.
Step-by-step explanation:
To find the probability that X is between 38 and 76, we need to find the area under the normal curve between these values. We can use the standard normal distribution and convert the values to z-scores.
The z-score for 38 is calculated as: z = (38 - 57) / 19 = -0.947.
The z-score for 76 is calculated as: z = (76 - 57) / 19 = 1.
Using a standard normal distribution table or a calculator, we can find the proportion of values between these two z-scores. The probability that X is between 38 and 76 is approximately 0.684.