Question

The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately normally distributed.

97.5% of the time, the bolt is inserted in less than which time value? Round to the nearest whole number.

Answer 1

Given that,

mean =  = 15

standard deviation =  = 4

Using standard normal table,

P(Z < z) = 97.5%

=(Z < z) = 0.975

= P(Z < z ) = 0.975  

z =1.96   

Using z-score formula  

x = z +

x = 1.96*4+15

x = 22.84

X=23