Number of Questions:
Marks Available:
Pass Percentage:
Time Allowed:
This exam is running in standalone mode. Your answers and marks will not be saved!

Paused

The Exam has been suspended. Press Resume to continue.

You will be able to resume this session the next time you start this activity.

Click on a question number to see how your answers were marked and, where available, full solutions.

Question Number Score
/
Total / (%)

Performance Summary

Exam Name:
Session ID:
Student's Name: ()
Exam Start:
Exam Stop:
Time Spent:

The exam has finished. You may now close this window.

The time,  in minutes between customer arrivals at the RyanJet check-in desk at Newcastle Airport follows an exponential distribution with rate 0.9 i.e. 

XExp(0.9)

a)

Find E[X] between customer arrivals at the RyanJet check-in desk at Newcastle Airport :

E[X]=? Expected answer: minutes (enter as a decimal correct to 3 decimal places).

Find Var(X):

Var(X)=? Expected answer: (enter as a decimal correct to 3 decimal places).

This feedback is on your last submitted answer. Submit your changed answer to get updated feedback.

b)

Find the probability that the time between two customers arriving is less than 1.7 minutes:

 P(X<1.7)=? Expected answer: (enter as a decimal correct to 3 decimal places)

This feedback is on your last submitted answer. Submit your changed answer to get updated feedback.

Advice

If XExp(λ) then E[X]=1λ and  Var(X)=1λ2.

Also P(X<a)=1eλa.

a)

If XExp(0.9) then:

E[X]=1λ=10.9=1.111 to 3 decimal places.

Var(X)=1λ2=10.92=1.235 to 3 decimal places.

b)

P(X<1.7)=1(e0.9×1.7)=1(e1.53)=0.783 to 3 decimal places.

\( \begingroup \)

A new supermarket plans to open somewhere on the outskirts of a town. In fact, $X$, the distance of a new supermarket from the town centre is Uniformly distributed between $\var{lower}$ metres and $\var{upper}$ metres i.e. 

\[X \sim \operatorname{U}(\var{lower},\var{upper})\]

a)

Find $\operatorname{E}[X]$, the expected distance in metres of the new supermarket from the town centre:

$\operatorname{E}[X]=\;?$ Expected answer: m  (to 3 decimal places).

Also find the variance $\operatorname{Var}(X)$:

 $\operatorname{Var}(X)=\;$? Expected answer: (to 3 decimal places).

 

This feedback is on your last submitted answer. Submit your changed answer to get updated feedback.

b)

Find the probability that the supermarket opens within $\var{thisdis}$ kilometres of the town centre.

$P(X \le \var{thisdis}\textrm{km})=\;$? Expected answer:  (to 3 decimal places).

This feedback is on your last submitted answer. Submit your changed answer to get updated feedback.

Advice

a) For a Uniform distribution \[X \sim \operatorname{U}(\var{lower},\var{upper})\] we have:

$\displaystyle \operatorname{E}[X] = \frac{\var{lower}+\var{upper}}{2}=\var{ans1}$m

$\displaystyle \operatorname{Var}[X] = \frac{(\var{upper}-\var{lower})^2}{12}=\frac{(\var{upper-lower})^2}{12}=\var{ans2}$ to 3 decimal places.

b)

$\displaystyle P(X \le \var{thisdis}\textrm{km})=\frac{\var{thisdis}\times 1000 -\var{lower}}{\var{upper}-\var{lower}}=\var{ans3}$ to 3 decimal places.

\( \endgroup \)