Question

5. [-/4.7 points) DETAILS BBUNDERSTAT126.8.015. ASK YOUR TEACHE Blood type AB is found in only 3% of the population. If 315 people are chosen at random, find the probability of the following. (Use the normal approximation. Round your answers to four decimal places.) (a) 5 or more will have this blood type (b) between 5 and 10 will have this blood type

Answer 1

P( Blood type AB) =0.03

Sample size, n= 315

Let X be the number of people with Blood Type AB

X~ Binomial( 315, 0.03)
Now, since the sample size is large and np >5 , we will use normal approximation to the Binomial distribution

X~ Normal ( np, np(1-p))

X~ Normal ( 9.15, 8.8755)

a) P(X >= 5) = P( X >4.5 ) ; Using continuity correction

= P( $\frac{X-\mu}{\sigma}$ > $\frac{4.5-9.15}{\sqrt{8.8755}}$ )

= P( z > -1.56)

= P( z < 1.56)

= 0.94062

b) P( 5 < X < 10) = P( 5.5 < X < 9.5) ; Using the continuity correction

= P( $\frac{5.5-9.15}{\sqrt{8.8755}}$ < $\frac{X-\mu}{\sigma}$ < $\frac{9.5-9.15}{\sqrt{8.8755}}$ )

= P( -1.22< z < 0.12)

= P( z < 0.12) - P(z < -1.22)

= P( z < 0.12) -1 + P(z < 1.22)

= 0.54776 - 1 + 0.88877

= 0.4365