Answer
The results of the survey are unusual. These results indicate that it may be a factor that will increase the occurrence of a self-injurious behavior.
Work Step by Step
The percentage of college students who had at least one incidence is 17% and hence \[\lambda =0.17\] and \[t=40\]. So, \[\mu =\lambda t=\left( 0.17 \right)\left( 40 \right)=6.8\]
Use the Poisson function to compute the required probability \[P\left( X\ge 12 \right)\]
Use Excel and follow the below steps:
Step 1: Select the Formulas > More Functions.
Step 2: Select Statistical > POISSON.DIST in menu.
Step 3: In the cell named X, enter the random variable value 12.
Step 4: Enter the mean value of 6.8.
Step 5: In the cell named cumulative, type TRUE.
The probability is obtained as 0.9779.
The probability that at least 12 is the complement of the probability, that is, fewer than 12. Therefore, the required probability \[P\left( X\ge 12 \right)\] is calculated as follows:
\[\begin{align}
& P\left( X\ge 12 \right)=1-P\left( X<12 \right) \\
& =1-0.9779 \\
& =0.0221
\end{align}\]
An event is said to be an unusual event when it has low chance or probability of happening. An event below 0.05 probability is considered as an unusual event. The probability that at least 12 of the college students had a history of emotional abuse is obtained as 0.0221 that is less than 0.05. Hence, it can be concluded that having at least 12 of the college students with the history of emotional abuse is unusual.
