The data set has size 80. Approximately how many observations lie within one standard deviation to either side of the mean?

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 and standard deviation , a large sample size, of size at least 30, can be approximated to a normal distribution with mean and standard deviation

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.

step-by-step explanation:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: