Q. 37 A small ferry runs every half ho... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 6: Q. 37 (page 378)

A small ferry runs every half hour from one side of a large river to the other. The number of cars $X$ on a randomly chosen ferry trip has the probability distribution shown below. You can check that $渭_{X} = 3.87$ and $蟽_{X} = 1.29$ .
(a) The cost for the ferry trip is $$ 5$ . Make a graph of the probability distribution for the random variable $M =$ money collected on a randomly selected ferry trip. Describe its shape.
(b) Find and interpret $渭_{M}$ .
(c) Compute and interpret $蟽_{M}$ .

Short Answer

Expert verified

(a) The distribution is left-skewed because the highest bar is to the right and the tail of smaller bars is to the left.

(b) $渭_{M} = 19.35$

Step by step solution

Part (a) Step 1: Given Information

The money collected is the product of the cost for the ferry trip $$ 5$ and the number of cars $X : $ M = 5 X$ The probabilities for $M$ are the same as the probabilities for $X $$ .

Part (a) Step 2: Explanation

Create a probability histogram

The width of the bars has to be equal and the height has to be equal to probability.

Part (b) Step 1: Given Information

Given

$渭_{X} = 3.87$

$蟽_{X} = 1.29$

Part (b) Step 2: Explanation

The money collected is the product of the cost of the ferry trip $$ 5$ and the number of cars $X : M = 5 X$ The probabilities for $M$ are the same as the probabilities for .

Properties mean and standard deviation:

localid="1649910106181"

$ 渭_{a X + b} = a 渭_{X} + b 蟽_{a X + b} = a 蟽_{X}

Then we obtain $f$ or $M$

localid="1649910148340"

M = 5 X : 渭_{M} = 渭_{5 X} = 5 渭_{X} = 5 (3.87) = 19.35

Part (c) Step 1: Given Information

Given

$渭_{X} = 3.87$

$蟽_{X} = 1.29$

Part (c) Step 2: Explanation

The money collected is the product of the cost for the ferry trip $$ 5$ and the number of cars localid="1649910262405" $X : $ M = 5 X$ The probabilities for $M$ are the same as the probabilities for $X$ .

Properties mean and standard deviation:

localid="1649910278936"

渭_{a X + b} = a 渭_{X} + b 蟽_{a X + b} = a 蟽_{X}

Then we obtain

f

M

localid="1649910308856"

M = 5 X : 蟽_{M} = 蟽_{5 X} = 5 蟽_{X} = 5 (1.29) = 6.45

The amount that the ferry collects varies on average about

$ 6.45

about the mean of

$ 19.35

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91影视

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Explanation

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