Question

Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area. Let X represent the number of customers on a randomly chosen trip.
Based on previous data, here is the probability distribution of X along with summary statistics:
X = # of customers 0 1 2 3
P(X) 0.10 0.20 0.30 0.40
Mean: μx = 2
Standard deviation: σx = 1
Suppose that each trip costs Marcos $1 in fuel regardless of how many customers he has, and each customer on a trip pays him $10. Let Y represent Marcos' net gain from a randomly chosen trip. What are the mean and standard deviation of Y?

Answer 1

Answer:

Mean y = 19 ; SD y = 10

Step-by-step explanation:

Given that:

No of customers : __ 0 ____ 1 _____ 2 ___ 3

P(x) : ___________0.10 __ 0.20 __0.30 _0.40

Fuel cost =$1 (constant)

Amount paid per customer =$10

Number of customers = x

σx = 1 ; μx = 2

σ^2 = 1^2 = 1

Mean of Y

μy = E(Y)

= E(10x - 1)

= 10(Ex) - 1

E(x) = 2

= 10(2) - 1

= 20 - 1

= 19

σY = SD(y)

SD(10x - 1)

10*SD(x) - 1

SD(x) = 1

10(1) - 0

Note : SD of a constant = 0

10 - 0

= 10

Answer 2

The mean of Y is 19 and the standard deviation of Y is 10 and this can be determined by using the given data.

Given :

• Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area.
• Let X represent the number of customers on a randomly chosen trip.
• Standard deviation: σx = 1
• Suppose that each trip costs Marcos $1 in fuel regardless of how many customers he has, and each customer on a trip pays him $10.
• Let Y represent Marcos' net gain from a randomly chosen trip.

The mean of Y can be calculated as given below:

$\rm \mu(Y)=E(Y)$

$\rm \mu(Y)=E(10x - 1)$

$\rm \mu(Y) = 10E(x) - 1$

According to the given data, the value of E(x) is 2. Substitute the value of E(x) in the above expression.

$\rm \mu(Y) = 10(2) - 1$

$\rm \mu(Y) = 19$

Now, the standard deviation of Y can be calculated as:

$\rm \sigma_Y=SD(Y)$

$\rm \sigma_Y=SD(10x-1)$

$\rm \sigma_Y=10SD(x)-SD(1)$

The value of SD for a constant is zero.

$\rm \sigma_Y=10(1)-0$

$\rm \sigma_Y = 10$

For more information, refer to the link given below:

https://brainly.com/question/12402189