Question

according to the u.s. census, of the u.s. population were born in their state of residence. in a random sample of americans, what is the probability that fewer than were born in their state of residence? round the final answer to at least four decimal places and intermediate -value calculations to two decimal places.

Answer 1

p = 0.675

n = 178

x = 108

z = \frac{x - np}{\sqrt{np(1-p)}} = \frac{108 - 178* 0.675}{\sqrt{178* 0.675(1-0.675)}}

z = -1.9443

z = - 1.94

P (z < -1.94) = 1- P (z < 1.94) = 1- 0.9738 = 0.0262

P(x < 108) = 0.0262

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