Question

the weights of items produces by a company are normally distributed w a mean of 5 oz and a stdev of .2 oz. what is the proportion of items that weight more than 4.6 oz?

what is the minimum weight of the heaviest 30% of all items produced

Answer 1

Solution :

Given that,

mean = = 5

standard deviation = = 0.2

a ) P (x > 4.6 )

= 1 - P (x < 4.6 )

= 1 - P ( x -  / ) < ( 4.6 - 5 / 0.2)

= 1 - P ( z <- 0.4 / 0.2 )

= 1 - P ( z < -2)

Using z table

= 1 - 0.0228

= 0.9772

Probability = 0.9772

b ) P( Z > z) = 30%

P(Z > z) = 0.30

1 - P( Z < z) = 0.30

P(Z < z) = 1 - 0.30

P(Z < z) = 0.70

z = 0.52

Using z-score formula,

x = z * +

x = 0.52 * 0.2 + 5

x = 5.104

The minimum weight = 5.10