To solve this problem, we can use the empirical rules associated with a normal distribution.
The empirical rule tells you what percentage of your data falls within a certain number of standard deviations from the mean:
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
In our dataset, the mean is 5.1 and standard deviation 0.9, therefore, the interval 4.2 to 5.1 represents half the area within one standard deviation. Since the normal distribution is symmetric and 68% of the data falls within one standard deviation, half of this data falls in our desired interval.
about 34% of the data falls between 4.2 and 5.1.