Question

es 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. For a randomly selected worker, what's the approximate probability the bolt will be inserted in 19 minutes or less? om ork O A. 19% OB. 18% O C. 16% OD. 84% & TO lan book Funch

Answer 1

Given the mean time for workers at a factory to insert a delicate bolt into an engine is $\mu$ = 15 minutes , the standard deviation as $\sigma$ = 4 and also the distribution is normal hence the probability is calculated using Z score.

Now P( X<= 19) is calculated by finding the Z score at X = 19 as:

X- Z 19 – 15 4

Thus P( X<=19) = P( Z< 1) is calculated using the excel formula for normal distribution which is =NORM.S.DIST(1, TRUE), thus the probability is calculated as 0.84.

Now converting into probability we get it as 0.84 *100 = 84%.

D) Thus the percentage is 84%.