Question

The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 40 minutes.

Answer 1

Answer: 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

$\lambda=\frac{1}{\mu}$

with μ as the mean.

The probability density distribution for this type of distribution is

$f(x)=\lambda e^{-\lambda x}$

And probability is calculated as

$P(X$

For tuning of an engine, the rate is

$\lambda=\frac{1}{40}$

λ = 0.025

a. Probability of less than 30 minutes:

$P(X$

$P(X$

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

$P(30$

$P(X$

$P(X$

P (X < 35) = 0.5831

P (X < 30) = 0.5276

Then:

$P(30$

P (30 < X < 35) = 0.0555

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