Please show work Based upon statistical studies it has been

Please show work.

Based upon statistical studies it has been found that 4.22% of all households in the United States in 2010 had a combined household income above $250,000. If 14,000 households from 2010 are selected at random, what is the probability that:

a) between 600 and 650 of them (inclusive) had a household income above $250,000?

b) at least 575 of them had a household income above $250,000?

Solution

probability of household above = 0.042

probability of household below = 0.958

a) between 600 - 650

we have to calculate p(600)+p(601)p(602)+..........+p(649)+p(650)

p(600 ) = 14000C600*(0.042)^600*(0.958)^13400

SIMILARLY WE CAN CALCULATE REST.

B) ATLEAST 575 = 1 - (P(0)+P(1)+........P(574))

AS ABOVE WE CAN CALCULATE THE PROBABILITY.