Answer:
Approximately 54 observation lie within one standard deviations of the mean.
Step-by-step explanation:
To solve this question, it is important to know the Central Limit Theorem and the Empirical Rule
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size, of size at least 30, can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s= \frac{\sigma}{\sqrt{n}}[/tex]
Empirical Rule
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Data set with size 80.
So the distribution will be approximately normal.
The empirical rule states that, for normally distributed random variable, 68% of the measures are within 1 standard deviation of the mean.
There are 80 observation
0.68*80 = 54.4
Approximately 54 observation lie within one standard deviations of the mean.
