Zainab runs her own business where she leads guided day-long tours for small groups of tourists in her city. Each tour has a maximum of 333 guests. Let XXX represent the number of customers Zainab gets on a randomly chosen day. Based on previous data, here is the probability distribution of XXX along with summary statistics: X=\text{\# of customers}X=# of customersX, equals, start text, \#, space, o, f, space, c, u, s, t, o, m, e, r, s, end text 000 111 222 333 P(X)P(X)P, left parenthesis, X, right parenthesis 0.200.200, point, 20 0.100.100, point, 10 0.400.400, point, 40 0.300.300, point, 30 Mean: \mu_X=1.8μ X =1.8mu, start subscript, X, end subscript, equals, 1, point, 8 Standard deviation: \sigma_X\approx1.08σ X ≈1.08sigma, start subscript, X, end subscript, approximately equals, 1, point, 08 It costs Zainab \$5$5dollar sign, 5 each day to pay for her own transportation to her business, and then each customer she gets pays her \$60$60dollar sign, 60. Let YYY represent Zainab's net gain on a randomly chosen day. What are the mean and standard deviation of YYY?

An

μ  Y=103 dollars  

σ  Y≈64.8 dollars

Step-by-step explanation:

We can find her income by multiplying the number of customers by 606060, and then subtracting her fixed transportation cost to get her net gain:

Y=60X-5Y=60X−5Y, equals, 60, X, minus, 5

How will this transformation impact the mean and standard deviation?

Hint #22 / 4

Effect on mean

Multiplying by 606060 and subtracting 555 both impact the mean:

\begin{aligned} \mu_Y&=60\left(\mu_X\right)-5 &=60\left(1.8\right)-5 &=108-5 &=103 \end{aligned}  

μ  

Y

=60(μ  

X

)−5

=60(1.8)−5

=108−5

=103

Hint #33 / 4

Effect on standard deviation

Multiplying by 606060 impacts the standard deviation, but subtracting 555 does not — adding or subtracting a constant only shifts data, which doesn't affect the spread.

\begin{aligned} \sigma_Y&=60\left(\sigma_X\right) &\approx60\left(1.08\right) &\approx64.8 \end{aligned}  

σ  

Y

=60(σ  

X

)

≈60(1.08)

≈64.8

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following