Answer: 1
Step-by-step explanation:
If a random variable x is uniformly distributed in [a,b] the
Mean =
Standard deviation :
Let x = Times required for a cable company to fix cable problems
As per given.
x is uniformly distributed between 40 minutes and 65 minutes.
Then , mean = minutes
Standard deviation : minutes
Consider , P (mean- 2(Standard deviation) < X < mean+2(Standard deviation) )
= P(52.5-2(7.22)< X < 52.5+2(7.22))
=P(38.06 <X < 66.94 ).
But x lies between 40 minutes and 65 minutes.
Also, [40 minutes, 65 minutes]⊂ [38.06 minutes , 66.94 minutes]
Therefore ,P(38.06 <X < 66.94 ) =1
∴ The probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean is 1.