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)

=

triangle abc is reflected on the line x=-6.5 then reflected again on the x axis

step-by-step explanation: