A Gold Canyon candle is designed to last nine hours. However, depending on the w

as probabilty for uniform function P(X7)=1-P(X

ID: 3208111 • Letter: A

Question

A Gold Canyon candle is designed to last nine hours. However, depending on the

wind, air bubbles in the wax, the quality of the wax, and the number of times the candle is relit,

the actual burning time (in hours) is a uniform random variable with a = 6.5 and b =

10.5. Suppose one of these candles is randomly selected.

a) Find the probability that the candle burns at least seven hours.

b) Find the probability that the candle burns at most eight hours.

c) Find the probability that the candle burns between seven and 10 hours.

d) Find the mean burning time of the candles.

e) Find the standard deviation of the burning time of the candles.

as probabilty for uniform function P(X<x) =(x-a)/(b-a)

a) probabilty that the candle burns at least seven hours =P(X>7)=1-P(X<7)=1-(7-6.5)/(10.5-6.5)

=1-0.5/4=3.5/4=7/8=0.875

b)probability that the candle burns at most eight hours=P(X<8)=(8-6.5)/(10.5-6.5)=1.5/4=0.375

c)probability that the candle burns between seven and 10 hours=P(7<X<10)=(10-7)/(10.5-6.5)=3/4=0.75

d) mean=(a+b)/2 =(6.5+10.5)/2 =8.5

e)standard deviation =(b-a)/(12)1/2 =(10.5-6.5)/(12)1/2=0.577

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.