Answer to Question #114062 in Statistics and Probability for Lethabo

Question

1.1 A batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours. Assuming a normal distribution: 1.1.1 how many lamps will fail before 900 hours? (5) 1.1.2 how many lamps will fail between 950 and 1000 hours? (5) 1.1.3 and given the same mean life, what would the standard deviation have to be to ensure that not more than 20% of lamps fail before 916 hours?

Answer 1

1.1.1 how many lamps will fail before 900 hours?

 Lamps that will fail before 900 hours is calculated as (900-1000)/75 or -100/75=-1.333

probability of z < = -1.33 is 0.0912

0.0912 *5000= 456 lamps.

1.1.2 how many lamps will fail between 950 and 1000 hours?

the lamps fail between 950 and 1000 hours is a z between -2/3 and 0.

950-1000/75= -0.667

That is a p-value of 0.2475

0.667* 5000 =1238 lamps.

1.1.3 and given the same mean life, what would the standard deviation have to be to ensure that not more than 20% of lamps fail before 916 hours?

the z-value for 20% is -0.84 from the table

standard deviation (sd)

-0.84*sd=(916-1000)

-0.84*sd=-84

standard deviation=100