Suppose we have a factory that produces lightbulbs and that each bulb independently has a 5% probability of dying after 4 years. suppose that during a particular year we produce 1250 bulbs. let x be the rv for the number of bulbs still working after 4 years. use the clt to approximate p(x > 1200).

0.4166

Step-by-step explanation:

Given that we have a factory that produces light bulbs and that each bulb independently has a 5% probability of dying after 4 years.

i.e. prob  = 0.05 for each bulb for dying since independent is given

Also there are only two outcomes either working or dying.

X no of bulbs still working is binomial with

constant probability p = 0.95, q = 0.05 and n = 1250

np =

nq = 62.5

Both are >5.  Hence X can be approximated to normal with

mean = 1187.5 and variance =npq = 59.375

std dev = 7.7055

Using central limit theorem we find that X is N(1187.8, 7.7055)

P(X > 1200)

=

step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.