Question

the annual stock of cereal (maize plus others) per household in Zambia is believed to follow a normal distribution with a mean of 373kg and a standard deviation of 185 kg
I. what is the probability that a randomly chosen household will stock at least 400kg of cereal?
ii) if it has been shown that a normal household will not run out of cereal in any given year, if it has stock of at least 250kg of cereal , what proportion if households would not run out?
iii) if 6.94% of households have stocks below a certain value, the government calls such a value critical, determine the critical value
iv)determine the proportion of house holds who have stocks within 100kg of mean

Answer 1

u = 373, = 185

z = (x-u)/

i) x = 400

z = (400-373)/185

Z = 0.146

P(x >= 400) = p(z >= 0.146)

= 0.4420

ii) x = 250

z = (250-373)/185

Z = -0.665

P(x >= 250) = p(z >= -0.665)

= 0.7470

iii) p = 0.0694 (6.94%)

Corresponding z score = -1.48 (for lower limit)

Thus, -1.48 = (x - 373)/185

x = 99.2 kg

iv) to determine proportion within 100kg from mean

Weight range is 273 to 473

Thus,

P( 273 < u < 373)

= P ( (273-373)/185 < z < (473-373)/185 )

= p( -0.54 < z< 0.54)

= 0.7054-0.2946

= 0.4108

Or 41.08%