A light bulb manufacturing process results in 6% of the light bulbs being defective. If 5 light bulbs are randomly
selected, find the probability that all of the light bulbs are
fully functioning.

Step-by-step explanation:

Given

Represent the event that a bulb is defective with p.

So:

Required

Determine the probability that all 5 are fully functioning

Represent the event that a bulb is defective with q.

So:

Make q the subject

Substitute 6% for p

Convert % to decimal

If 5 were selected and all are functioning, the event is represented as: q q q q q

And the probability is:

Substitute 0.94 for q

--- approximated

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.