Question

Use the table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.

A manufacturer of light bulbs finds that one light bulb model has a mean life span of 1028 h with a standard deviation of 86 h. What percent of these light bulbs will last as follows? (Round your answers to one decimal place.)

(a) at least 940 h
%

(b) between 850 and 900 h
%

Answer 1

solution

P(x >940 ) = 1 - P(x< 940)

=1- P[(X- ) / < (940-1028) / 86]

=1- P(z <-1.02 )

Using z table

=1-0.1539

=0.8461

answer=84.6%

(B)

P(850< x <900 ) = P[(850-1028) / 86 < (x - ) / < (900-1028) / 86 )]

= P(-2.07 < Z <-1.49 )

= P(Z <-1.49 ) - P(Z < -2.07)

Using z table   

= 0.0681-0.0192

= 0.0489

answer=4.9%