Answer: 505
Step-by-step explanation:
The formula to find the sample size n , if the prior estimate of the population proportion (p) is known:
[tex]n= p(1-p)(\dfrac{z}{E})^2[/tex] , where E= margin of error and z = Critical z-value.
Let p be the population proportion of crashes.
Prior sample size = 250
No. of people experience computer crashes = 75
Prior proportion of crashes [tex]p=\dfrac{75}{250}=0.3[/tex]
E= 0.04
From z-table , the z-value corresponding to 95% confidence interval = z=1.96
Required sample size will be :
[tex]n=0.3(1-0.3)(\dfrac{1.96}{0.04})^2[/tex] (Substitute all the values in the above formula)
[tex]n= (0.21)(49)^2= 0.21\times2401[/tex]
[tex]n= 504.21\approx505[/tex] (Rounded to the next integer.)
∴ Required sample size = 505
