Question

A manufacturer of light bulbs finds that one light bulb model has a mean life span of 1025 h with a standard deviation of 80 h. What percent of these light bulbs will last as follows? (Round your answers to one decimal place.)

(a) at least 970 h
%

(b) between 810 and 880 h

%

Answer 1

Solution :

Given ,

mean = = 1025

standard deviation = = 80

P(x >970 ) = 1 - P(x<970 )

= 1 - P[(x -) / < (970-1025) / 80]

= 1 - P(z <-0.69 )

Using z table

= 1 - 0.2451

=0.7549

answer=75.5%

(B)

P(810< x <880 ) = P[(810-1025) /80 < (x - ) / < (880-1025) / 80)]

= P( -2.69< Z <-1.81 )

= P(Z <-1.81 ) - P(Z <-2.69 )

Using z table   

= 0.0351-0.0036

=0.0315

answer=3.2%