Questions: In binomial experiments, each trial can be viewed as having only two outcomes. True

Solution Steps

The question asks whether the formula for computing \( z \) is the same for a single data value as it is for an average of the data values for a sample group.

For a single data value, the \( z \)-score is calculated as:

\[ z = \frac{x - \mu}{\sigma} \]

where \( x \) is the data value, \( \mu \) is the population mean, and \( \sigma \) is the population standard deviation.

For a sample mean, the \( z \)-score is calculated as:

\[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \]

where \( \bar{x} \) is the sample mean, \( \mu \) is the population mean, \( \sigma \) is the population standard deviation, and \( n \) is the sample size.

The formulas are not the same due to the presence of the standard error term \(\frac{\sigma}{\sqrt{n}}\) in the formula for the sample mean.

The question asks whether in binomial experiments, each trial can be viewed as having only two outcomes.

In a binomial experiment, each trial indeed has only two possible outcomes, typically referred to as "success" and "failure."

Final Answer