Answer:
405
Step-by-step explanation:
To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.
[tex]n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q }{E^2}[/tex]
The values that are given are p = 0.84 and E = 0.03.
You can solve for the critical value which is equal to the z-score of (1 - confidence level)/2. Use the calculator function of invNorm to find the z-score. The value will given with a negative sign, but you can ignore that.
(1 - 0.9) = 0.1/2 = 0.05
invNorm(0.05, 0, 1) = 1.645
You can also solve for q which is 1 - p. For this problem q = 1 - 0.84 = 0.16
Plug the values into the equation and solve for n.
[tex]n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333[/tex]
Round up to the next number, giving you 405.
