Calculating Number of Trials in Binomial Test with Probability 1/2
The question provided in the image asks to find the value of \( n \) in a binomial test where \( p = 1/2 \), \( p \cdot n = 35 \), and \( q \cdot n = 35 \) as well. Here, \( p \) is the probability of success on a single trial, \( q \) is the probability of failure on a single trial, and \( n \) is the number of trials.
Since \( p = 1/2 \), this means that \( q \), the probability of failure, must also be equal to \( 1/2 \) since \( p + q = 1 \).
Given \( p \cdot n = 35 \), and we know \( p = 1/2 \), we can solve for \( n \) as follows:
\[ 1/2 \cdot n = 35 \]
Now, to find \( n \), we multiply both sides of the equation by 2:
\[ n = 2 \cdot 35 \]
\[ n = 70 \]
Therefore, \( n \), the number of trials, is 70.
