Question

a packing plant fills bags with cement. the weight X kg of a bag can be modeled normal distribution with mean 50kg and standard deviation 2kg.

a) Find the probability that a randomly selected bag weighs more than 53 kg.

b)find the weight that exceed by 98% of the bags

c)3 bags are selected randomly. Find the probability that two weigh more than 53 kg and one weigh less than 53kg

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 2

(a) P(x > 53) = 1 - P(x < 53)

= 1 - P((x - ) / < (53 - 50) / 2)

= 1 - P(z < 1.5)

= 1 - 0.9332   

= 0.0668

Probability = 0.0668

(b)

P(Z > z) = 98%

1 - P(Z < z) = 0.98

P(Z < z) = 1 - 0.98 = 0.02

P(Z < -2.05) = 0.02

z = -2.05

Using z-score formula,

x = z * +

x = -2.05 * 2 + 50 = 45.9

Weight = 45.9 kg

(c)

n = 3

= 50 and

= / n = 2 / 3 = 1.1547

P( > 53) = 1 - P( < 53)

= 1 - P(( - ) / < (53 - 50) / 1.1547)

= 1 - P(z < 2.598)

= 1 - 0.9953

= 0.0047

P(x < 53) = P((x - ) / < (53 - 50) / 2)

= P(z < 1.5)

= 0.9332

Probability = 0.0047 + 0.9332 = 0.9379