Answer: 0.0062
Step-by-step explanation:
Let X represent the number with influenza in the sample.
As per given , we have
p= 0.20
n= 400
then,
[tex]\mu=np=400\cdot0.20=80\\\\\sigma=\sqrt{np(1-p)}\\\\=\sqrt{400(0.2)(0.8)}=8[/tex]
[tex]x=400\cdot0.25=100[/tex]
z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{100-80}{8}=2.5[/tex]
The probability that at least 25% of the sample is observed to have influenza:
[tex]P(p\geq0.25)=P(z\geq2.5)=1-P(z<2.5)\\\\=1-0.9937903=0.0062097\approx0.0062[/tex] Â [using p-value calculator ]
Hence, the probability that at least 25% of the sample is observed to have influenza = 0.0062
