We are estimating the spares requirement for a radar power supply. The power supply was designed with a mean ($\mu$) life of $6500$ hours. The standard deviation ($\sigma$) determined from testing is $750$ hours. What is the likelihood that a power supply would fail between $7225$ and $7500$ hours?
a. $0.4082$ or $40.82\%$
b. $0.0742$ or $7.42\%$
c. $0.3340$ or $33.40\%$
d $0.1066$ or $10.66\%$
Consider:
Experiment: Randomly select one power supply
Random Variable $L$: Power Supply $L$ifetime
Possible Values $l$: [0 hours,1300 hours]
Determine: $P$($7,225 \le$ $L$ $\le$ $7,550$) $=$ $P$($\dfrac{7,225-6,500}{750}$ $\le$ $Z$ $\le$$\dfrac{7,500-6,500}{750}$)
$=$ $P$(0.97 $\le$ $Z$ $\le$ $1.33$) $= 0.9082 - 0.8340 =0.0742. $