2. 3. The life of light bulbs is distributed normally. The variance of the lifet

Question

2.
3.
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for between 547 and 580 hours. Round your answer to four decimal places. Answer 2 Points Keypad If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key Normal Table-o to-z Normal Table- to z

Explanation / Answer

Ans:

1)mean=530,standard deviation=sqrt(625)=25

z(547)=(547-530)/25=0.68

z(580)=(580-530)/25=2

P(0.68<z<2)=P(z<2)-P(z<0.68)

=0.9772-0.7517=0.2255

2)mean=80,standard deviation=7

z(69)=(69-80)/7=-1.571

z(84)=(84-80)/7=0.571

P(-1.571<z<0.571)=P(z<0.571)-P(z<-1.571)

=0.7161-0.0580=0.6581

3)mean=148,standard deviation=sqrt(49)=7

sample size,n=41

standard error of mean=7/sqrt(41)

z=(145.3-148)*sqrt(41)/7=-2.47

P(z<-2.47)=0.0068

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