Question

Estimate the probability of getting exactly 43 boys in 90 births. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Round to four decimal places. A. 0.0768 B. 0.0159 C. 0.0729 D. 0.1628

Answer 1

Answer:z=0.0768

Explanation:

For Binomial distribution

mean
`(\mu )=np`

Where n=90

and probabilty of getting success(P)=0.5 (also q=0.5)

`\mu =90* 0.5=45`

`√(Variance)=npq`

`√(Variance)=90* 0.5* 0.5=22.5`

Standard deviation
`(\sigma )=4.743`

Now using normal distribution as an approximation to the binomial distribution

`P(x=43)=P\left [ (42.5-45)/(4.743)<z<(43.5-45)/(4.743)\right ]`

Using standard normal tables P
`\left [ -0.527<z<-0.316 \right ]`

Value z=0.0768