Osram claims that the average life of its 75-watt lightbulb is 1,000 hours (sour

Question

Osram claims that the average life of its 75-watt lightbulb is 1,000 hours (source: Osram.com). Assume that the life of all such bulbs has a normal distribution with mean 1,000 hours, and standard deviation 70 hours. Determine the probability the mean life time of a random sample of 49 bulbs will be:

a)At least 985 hours.

b)Between 985, and 990 hours.

Determine the probability the mean life time of a random sample of 49 bulbs will be:

c)Within 18 hours of the population mean.

d)Less than the population mean by 15 hours

Explanation / Answer

here mean =1000

and std error of mean for a sample of 49 =std deviation/(n)1/2 =10

a)hence P(X>985) =1-P(X<985) =1-P(Z<(985-1000)/10) =1-P(Z<-1.5) =1-0.0668 =0.9332

b) P(985<X<990) =P((985-1000)/10<Z<(990-1000)/10) =P(-1.5<Z<-1) =0.9332-0.8413 =0.0918

c)P(-18<X-mean<18) =P(-18/10<Z<18/10) =P(-1.8<Z<1.8) =0.9641 -0.0359 =0.9281

d) P(-X-mean<-15) =P(Z<-15/10) =P(Z<-1.5) =0.0668

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

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