Solution :
It is given that :
Total number of adults in the sample of Ohio, n = 1500
Increase in the sale tax = 5% to 6 %
Let [tex]$\hat p$[/tex] = proportion of the adults that supported the increase in the sales tax.
= 40%
= 0.40
Therefore the probability that [tex]$\hat p$[/tex] will be more than 50% will be :
[tex]$P(\hat p > 0.50) = P\left( \frac{\hat p - E(\hat p)}{\sigma_{\hat p}} > \frac{0.50-0.40}{0.0123}\right)$[/tex]
[tex]$=P(z>7.936508)$[/tex]
[tex]$=1-P(Z<7.936508)$[/tex]
= 1 - 1
= 0
