Question

11. Find the area, to the nearest thousandth, of the indicated region of the standard normal distribution.

The region where z < −0.88

___square unit

12. Find the area, to the nearest thousandth, of the indicated region of the standard normal distribution.

The region where z < 2.57

_____square unit

13.Use the z-score 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 1023 h with a standard deviation of 88 h. What percent of these light bulbs will last as follows? (Round your answers to one decimal place.)

(a) at least 980 h
____%

(b) between 810 and 880 h
______ %

Answer 1

Solution

Given that

Using standard normal table

11 ) P ( Z < −0.88 ) = 0.1894

Probability =0.189

12 ) P ( Z < 2.57 ) = 0.9949

Probability =0.995

13 ) Given that,

mean = = 1023

standard deviation = = 88

a ) P (x > 980 )

= 1 - P (x < 980 )

= 1 - P ( x -  / ) < ( 980 - 1023 / 88 )

= 1 - P ( z < -43 / 88 )

= 1 - P ( z < -0.49 )

Using z table

= 1 - 0.3121

=0.6879

Probability = 0.6879 = 68.79%

b ) P (810 < x < 880 )

P ( 810- 1023 / 88 ) < ( x -  / ) < ( 880 - 1023 / 88 )

P ( -213 / 88 < z <-143 / 88 )

P (-2.42 < z < -1.62 )

P ( z < -1.62 ) - P ( z < -2.42 )

Using z table

= 0.0526 - 0.0078

= 0.0448

Probability = 0.0448 = 4.48%