The lifetimes of batteries from a manufacturer’s production process have a norma

Question

The lifetimes of batteries from a manufacturer’s production process have a normal distribution with mean 2000 hours and a standard deviation of 200 hours. What is the probability that a random battery from the production process fails to last at least 1100 hours? Make sure you define clearly your random variable and specify its distribution completely, including its parameter/s.

Refer to Problem #1 again. The manufacturer decides that any battery from the production process whose lifetime is less than the lower specification limit (LSL) will be considered defective and will be discarded. If the manufacturer wants the proportion of defective batteries to be only 0.5% of the production output, what should LSL be?

Explanation / Answer

Answer:

The lifetimes of batteries from a manufacturer’s production process have a normal distribution with mean 2000 hours and a standard deviation of 200 hours. What is the probability that a random battery from the production process fails to last at least 1100 hours? Make sure you define clearly your random variable and specify its distribution completely, including its parameter/s.

X is normal distribution with mean 2000 hours and a standard deviation of 200 hours

Z value for 1100, z =(1100-2000)/200 = -4.5

P( x <1100) = P( z < -4.5)

=0.0000

Refer to Problem #1 again. The manufacturer decides that any battery from the production process whose lifetime is less than the lower specification limit (LSL) will be considered defective and will be discarded. If the manufacturer wants the proportion of defective batteries to be only 0.5% of the production output, what should LSL be?

Z value for bottom 0.5% = -2.576

X= mean+z*sd = 2000-2.576*200 =1484.8

LSL= 1484.8

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.