Final answer:
Approximately 95 percent of the observations in a data set lie within two standard deviations from the mean.
Step-by-step explanation:
According to the Empirical Rule, approximately 95 percent of the observations in a data set lie within two standard deviations from the mean. So, in a data set with a size of 50, we can expect that approximately 95 percent of the observations lie within 2 standard deviations to either side of the mean.
In this case, the mean is given as 15 and the standard deviation is given as 4.3. To calculate the range of observations within 2 standard deviations, we multiply the standard deviation by 2 and add/subtract this value from the mean. So, the range would be 15 ± (2 * 4.3), which is equivalent to 15 ± 8.6. Therefore, the observations within 2 standard deviations would be between 6.4 and 23.6.