The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 40 minutes. a. What is the probability of tuning an engine in 30 minutes or less?

b. What is the probability of tuning an engine between 30 and 35 minutes?

a. P (x<30) = 0.5276

              b. P (30<x<35) = 0.0555

Step-by-step explanation: An exponential distribution is a distribution of time in which events happens at a constant average rate.

The rate is calculated as

with μ as the mean.

The probability density distribution for this type of distribution is

And probability is calculated as

For tuning of an engine, the rate is

λ = 0.025

a. Probability of less than 30 minutes:

P (X < 30) = 0.5276

Probability of tuning in 30 minutes or less is 52.76%.

b. Probability of between 30 and 35 can be described as

P (X < 35) = 0.5831

P (X < 30) = 0.5276

Then:

P (30 < X < 35) = 0.0555

Probability of tuning an engine between 30 and 35 minutes is 5.55%.

marco saved more.   he saved $35 more.

step-by-step explanation:

1+2+3+4+5+6+7+8+9+10 = 55

2*10 = 20

55-20 = 35

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2