Answer: 0.2643
Step-by-step explanation:
Given : The proportion of adults are unemployed : p=0.077
The sample size = 300
By suing normal approximation to the binomial , we have
[tex]\mu=np=300\times0.077=23.1[/tex]
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{300\times0.077(1-0.077)}\\\\=4.61749932323\approx4.62[/tex]
Now, using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponding to 26 will be :-
[tex]z=\dfrac{26-23.1}{4.62}\approx0.63[/tex]
Using standard distribution table for z , we have
P-value=[tex]P(z\geq0.63)=1-P(z<0.63)[/tex]
[tex]=1-0.7356527=0.2643473\approx0.2643[/tex]
Hence, the probability that at least 26 in the sample are unemployed =0.2643
