Answer:
[tex]P(x>99)= 0.468[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size 157
Sample mean
[tex]\=x =np[/tex]
[tex]\=x =157*0.56[/tex]
[tex]\=x = 87.92[/tex]
Generally the equation for Standard deviation is mathematically given by
[tex]\sigma=\sqrt{npq}[/tex]
[tex]\sigma=\sqrt{157*0.56*0.44}[/tex]
[tex]\sigma =6.22[/tex]
Therefore
[tex]P(x>99)=P(z>(\frac{99.5-87.92)}{6.22})[/tex]
[tex]P(x>99)=P(z>1.86)[/tex]
[tex]P(x>99)= 0.468[/tex]
