Question

The Tesla Model X is an electric car that can travel approximately 238-295 mi on a full charge. Tesla dealers claim the time it takes to fully recharge depends on the percent depleted, but is approximately a normal random variable X with mean u = 2.5 hours and standard deviation o = 0.75 hour (on a 240-volt line). Suppose a random Tesla Model X is connected to a home recharging station.

Answer 1

for normal distribution z score =(X-μ)/σx
mean μ=	2.5
standard deviation σ=	0.75

c)

probability =P(X<0.5)=(Z<(0.5-2.5)/0.75)=P(Z<-2.67)=0.0038

d)

probability =P(X>3)=P(Z>(3-2.5)/0.75)=P(Z>0.67)=1-P(Z<0.67)=1-0.74751=0.2525

P(all three have greater than 3) = (0.2525)^3=0.0161

e)

P(X =3.5 )=0 (since on a continuous distribution, point probability is 0)