Question

The breaking strength of a cable is known to be normally distributed with a mean of 4,000 kg and a standard deviation of 75 kg. The manufacturer wants at least 98% of its products to meet a stated minimum strength. The minimum strength specification that the manufacturer should use is approximately what?

Answer 1

Solution:-

Given that,

mean = = 4000

standard deviation = = 75

Using standard normal table,

P(Z > z) = 98%

= 1 - P(Z < z) = 0.98  

= P(Z < z) = 1 - 0.98

= P(Z < z ) = 0.02

= P(Z <-2.05 ) = 0.02  

z = -2.05 ( using z table )

Using z-score formula,

x = z * +

x = -2.05* 75+4000

x = 3846.25

x=3846 rounded