The electric-vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle's battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between 90 and 120 minutes. a. Give a mathematical expression for the probability density function of battery recharging time for this scenario. 1 -{₁ 0 A. f(x) = B. f(x) = = c. f(x) = 30 15 0 for 90 ≤ x ≤ 120 elsewhere for 90 ≤ x ≤ 120 elsewhere for 90 ≤ x ≤ 105 elsewhere 15 0 The correct answer is: A b. What is the probability that the recharge time will be less than 110 minutes (to 3 decimals)? c. What is the probability that the recharge time required is at least 100 minutes (to 3 decimals)? d. What is the probability that the recharge time required is between 95 and 110 minutes (to 3 decimals)?
The electric-vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle's battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between 90 and 120 minutes. a. Give a mathematical expression for the probability density function of battery recharging time for this scenario. 1 -{₁ 0 A. f(x) = B. f(x) = = c. f(x) = 30 15 0 for 90 ≤ x ≤ 120 elsewhere for 90 ≤ x ≤ 120 elsewhere for 90 ≤ x ≤ 105 elsewhere 15 0 The correct answer is: A b. What is the probability that the recharge time will be less than 110 minutes (to 3 decimals)? c. What is the probability that the recharge time required is at least 100 minutes (to 3 decimals)? d. What is the probability that the recharge time required is between 95 and 110 minutes (to 3 decimals)?
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Transcribed Image Text:The electric-vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a
nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle's battery (Tesla company website). Assume
that the actual recharging time required is uniformly distributed between 90 and 120 minutes.
a. Give a mathematical expression for the probability density function of battery recharging time for this scenario.
1
-{₁
0
A. f(x) =
B. f(x) =
=
c. f(x) =
30
15
0
for 90 ≤ x ≤ 120
elsewhere
for 90 ≤ x ≤ 120
elsewhere
for 90 ≤ x ≤ 105
elsewhere
15
0
The correct answer is:
A
b. What is the probability that the recharge time will be less than 110 minutes (to 3 decimals)?
c. What is the probability that the recharge time required is at least 100 minutes (to 3 decimals)?
d. What is the probability that the recharge time required is between 95 and 110 minutes (to 3 decimals)?
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