Question

Q2a).. The income of families in a slum have a normal distribution with a mean of $ 52 per year and a standard deviation of $ 5 . find (10mks)
i)Percentage of families with an income of more than $50 per year
ii). Percentage of families with an income of between $ 48 and $ 54 per year
iii) .In a sample of 500 families in this slum, how many have an income of more than $ 50 per year?

Answer 1

i)

$P(Income>50) = 1 - P(Income \le 50) = 1 - F((50-52)/5) = 1 - F(-0.4) = F(0.4) = 0.6554$

ii)

$P(48<Income\le54) = P(Income \le 54) - P(Income\le48) = \\ =F((54-52)/5) - F((48-52)/5) = F(0.4) - F(-0.8) = \\=0.6554 - 0.2119 = 0.4436$

iii)

n*p = 500*P(Income>50) = 500*0.6554 = 327.7 $\approx$ 328

Approximately 328 families of 500 have an income of more than $50 per year.