Answer:
116 students
Step-by-step explanation:
The standard deviation for a proportion is:
[tex]s=\sqrt{\frac{(1-p)*p}{n}}[/tex]
For any measured sample proportion x, the z score is given by:
[tex]z = \frac{x-p}{s}[/tex]
The population proportion is 0.53
At the 14th percentile, the corresponding z-score is z =-1.08.
Since 0.48 is at the 14th percentile, the standard deviation is:
[tex]-1.08=\frac{0.48-0.53}{s}\\ s=0.46296[/tex]
Therefore, the sample size 'n' is given by:
[tex]0.046296=\sqrt{\frac{(1-0.53)*0.53}{n}}\\n=\frac{0.47*0.53}{0.046296^2}\\n= 116\ students[/tex]
The sample size must have been of 116 students.
