Assume 49% of us have Group O blood. A hospital is conducting a blood drive beca

Question

Assume 49% of us have Group O blood. A hospital is conducting a blood drive because its supply of Group O blood is low, and it needs at least 171 donors of Group O blood. If 335 volunteers donate blood, estimate the probability that the number with Group O blood is at least 171. Is the pool of 335 volunteers likely to be sufficient?

(a) P(X171)=

(Round to four decimal places as needed.)

(b) What does the result from part (a) suggest?

A. The pool is likely to be sufficientThe pool is likely to be sufficient because P(171) is less than 50 %.

B. The pool is not likely to be sufficientThe pool is not likely to be sufficient because P(x171) is less than 50 %.

C. The pool is likely to be sufficientThe pool is likely to be sufficient because P(x171) is more than 50 %.

D. The pool is not likely to be sufficientThe pool is not likely to be sufficient because P(x171) is more than 50 %.

Explanation / Answer

P = 0.49

n = 335

p (x) = C(n,x) * p^x * (1-p)^(n-x)

Question a)

This is the case of normal approximation to binomial distribution.

P ( x>= 171)

By using correlation factor we get,

P (x>= 170.5)

Mean = np = 335*0.49 = 164.15

Standard deviation = sqrt (npq) = sqrt (335*0.49*(1-0.49)) = 9.1497

Z = ( x – Mean ) / Standard deviation

= (170.5 – 164.15) / 9.1479

= 0.69

P ( z > 0.69 ) = 1 – P ( z < 0.69 )

                       = 1 - 0.7549

                       = 0.2451

Answer:

0.2451

Question b)

Answer:

Option B

The pool is not likely to be sufficient. The pool is not likely be to be sufficient because P (x>= 171) is less than 50%

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