Answer :
Answer:
0.9689
Step-by-step explanation:
Given:
banks in Switzerland are private organizations, p = 51% = 0.51
Sample size, n = 544 banks
To find:
Probability (the sample proportion of private banks will be greater than 47%)
Now,
Mean of the sample, μ = np = 544 × 0.51 = 277.44
[tex]\bar{x}[/tex] = 544 × 0.47 = 255.68
Standard deviation = [tex]\sqrt{np(1-p)}[/tex]
or
Standard deviation = [tex]\sqrt{544\times0.51(1-0.51)}[/tex]
or
Standard deviation = 11.6595
Now,
[tex]P(\bar{x}\geq 47\%)[/tex]
= [tex]P(z\geq \frac{\bar{x}-\mu}{\sigma})[/tex]
= [tex]1- P(z\leq \frac{\bar{x}-\mu}{\sigma})[/tex]
= [tex]1- P(z\leq \frac{255.68-277.44}{11.6595})[/tex]
= [tex]1- P(z\leq -1.8662)[/tex]
Now, from standard z value table, we get
= 1 - 0.031021
= 0.9689