Answer:z=0.0768
Step-by-step explanation:
For Binomial distribution
mean [tex](\mu )=np[/tex]
Where n=90
and probabilty of getting success(P)=0.5 (also q=0.5)
[tex]\mu =90\times 0.5=45[/tex]
[tex]\sqrt{Variance}=npq[/tex]
[tex]\sqrt{Variance}=90\times 0.5\times 0.5=22.5[/tex]
Standard deviation[tex](\sigma )=4.743[/tex]
Now using normal distribution as an approximation to the binomial distribution
[tex]P(x=43)=P\left [ \frac{42.5-45}{4.743}<z<\frac{43.5-45}{4.743}\right ][/tex]
Using standard normal tables P[tex]\left [ -0.527<z<-0.316 \right ][/tex]
Value z=0.0768
