Twenty five heat lamps are connected in a greenhouse so, that when one lamp fails, another takes over immediately (only one lamp is turned on at any time.) The lamps operate independently, each with mean lifetime of 50 hours, and standard deviation of 4 hours. If the greenhouse is not checked for 1300 hours after the lamp system is turned on, what is the probability, that a lamp will be burning at the end of the 1300-hour period?

P = 0.006

Step-by-step explanation:

Given

n = 25 Lamps

each with mean lifetime of 50 hours and standard deviation (SD) of 4 hours

Find probability that the lamp will be burning at end of 1300 hours period.

As we are not given that exact lamp, it means we have to find the probability where any of the lamp burning at the end of 1300 hours, So we have

Suppose i represents lamps

P (∑i from 1 to 25 ( > 1300)) = 1300

= P(> )                  where represents mean time of a single lamp

= P (Z> )                Z is the standard normal distribution which can be found by using the formula

Z = Mean Time () - Life time of each Lamp (50 hours)/ (SD/)

Z = (52-50)/(4/) = 2.5

Now, P(Z>2.5) = 0.006 using the standard normal distribution table

Probability that a lamp will be burning at the end of 1300 hours period is 0.006

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.