Question

Light bulbs are found to have a mean life of 800 hours. The standard deviation is 160. A sample of 400 is chosen. Find the probability that 798 < x < 802

Answer 1

Solution :

Given that,

mean = $\mu$ = 800

standard deviation = $\sigma$ = 160

n = 400

$\mu$$\bar x$ =800

$\sigma$_{$\bar x$ =} $\sigma$ / $\sqrt$ n = 160 $\sqrt$ 400 = 8

P (798 < x < 802 )

P ( 798 - 800 / 8) < ( $\bar x$ - $\mu$ $\bar x$ /$\sigma$$\bar x$) < ( 802 - 800 / 8)

P (- 2 / 8< z < 2 / 8 )

P (-0.25 < z < 0.25 )

P ( z < 0.25 ) - P ( z < -0.25)

Using z table

= 0.5987 - 0.4013

= 0.1974

Probability = 0.1974