Chapter 6.2, Problem 39E

(a)

To determine

To Construct: a graph of the probability and explain its shape

Explanation of Solution

Given:

Number of passengers (Y)	35	36	37	38	39	40
Probability P(y)	0.10	0.10	0.30	0.35	0.10	0.05

Y= number of passengers

Calculation:

There are 4 crews there on each flight so

X=Y+4

Number of passengers (X)	39	40	41	42	43	44
Probability P(x)	0.10	0.10	0.30	0.35	0.10	0.05

Graph:

  

The distribution is not symmetric, highest bars in the middle at X=42 which is single peak lowest bars is at the end at X=44.

(b)

To determine

To Calculate: the ${\mu }_X$ and explain it

Answer to Problem 39E

  ${\mu }_X=41.4$

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_Y=37.4\\ {\sigma }_Y=1.24\end{array}$

Calculation:

Y= number of passengers

There are 4 crews there on each flight so

X=Y+4

Adding the constant to every data value, then the center of the distribution is also increased by that constant value

  $\begin{array}{c}{\mu }_X={\mu }_Y+4\\ =37.4+5\\ =41.4\end{array}$

If adding the constant value to every data it will increased the center of the distribution so 41.4 average numbers of people (passengers + crew) will be randomly selected.

(c)

To determine

To Calculate: the ${\sigma }_X$ and explain it

Answer to Problem 39E

  ${\sigma }_X=1.24$

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_Y=37.4\\ {\sigma }_Y=1.24\end{array}$

Calculation:

Y= number of passengers

There are 4 crews there on each flight so

Adding the constant to every data value, then the spread of the distribution will not affect, it remains unchanged.

  ${\sigma }_X={\sigma }_Y=1.24$

If adding the constant value to every data , then it will not affect the spread of the distribution so the number of people (passengers + crew) for a arbitrary selected flight varies on average 1.24 about the mean = 41.4 people.