An electrical firm manufactures 100-watt light bulbs. These bulbs, according to specifications written on the package, have a mean life of 900 hours with a standard deviation of 50 hours. Assume that the distribution is symmetric about the mean. a) Give an upper bound to the probability that the life of a bulb win a new production batch will exceed 990 hours. b) Suppose that the mean is unknown but the standard deviation is 50 hours. What can be said about the probability that the life of a new bulb will be within 150 hours of the unknown mean for that batch? c) How many new bulbs should be made so as to ensure, with probability at least 0.75, that the average life would be within 25 hours of the unknown mean? Assume each bulb is produced independently.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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