statistics probability

Question

Blood type AB is found in only 3% of the population.If 320 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

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(b) between 5 and 10 will have this blood type

Answer 1

Find np as (320)(0.03) or 9.6.

Find nq as (320)(1 − 0.03) or 310.4.

With 9.6 & 310.4 both at least 5, the Binomial Distribution here

can be approximated by the Normal Distribution.

Mean μ is given by np or 9.6 found above.

Standard Deviation σ is found by √(npq)

or (320 × 0.03 × 0.97)^0.5 or √9.312.

For Pr(X ≥ 5), write z = (5 − 9.6) / √9.312

or -1.507427202 which returns normal

probability by calculator program as

-0.4341494047.

Then Pr(X ≥ 5) is |-0.4341494047| + 0.5

or 0.9341494047 equivalent to 0.9341.

For Pr(5 ≤ X ≤ 10), determine z = (10 − 9.6) / √9.312

or 0.1310806263 which gives normal probability as

0.05214423655. Then take Pr(5 ≤ X ≤ 10) as

|-0.4341494047| + 0.05214423655 or 0.4862936412

equivalent to 0.4863.