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JT has two jobs: mowing yards and washing cars. Let [tex]\( X \)[/tex] represent the weekly earnings for mowing yards, and [tex]\( Y \)[/tex] represent the weekly earnings for washing cars. The mean of [tex]\( X \)[/tex] is \[tex]$60, and the mean of \( Y \) is \$[/tex]35.

Which answer choice correctly calculates and interprets the mean of the sum, [tex]\( S = X + Y \)[/tex]?

A. [tex]\( \mu_S = 47.5 \)[/tex]; next week, JT will earn \[tex]$47.5.
B. \( \mu_S = 47.5 \); JT can expect to earn \$[/tex]47.5, on average, in a typical week.
C. [tex]\( \mu_S = 95 \)[/tex]; next week, JT will earn \[tex]$95.
D. \( \mu_S = 95 \); JT can expect to earn \$[/tex]95, on average, in a typical week.



Answer :

GinnyAnswer
To solve this problem, we need to find the mean of the sum of JT's weekly earnings from both jobs. Let's denote:

- [tex]\( \mu_X \)[/tex] as the mean of JT's weekly earnings for mowing yards.
- [tex]\( \mu_Y \)[/tex] as the mean of JT's weekly earnings for washing cars.
- [tex]\( \mu_S \)[/tex] as the mean of the total weekly earnings, where [tex]\( S = X + Y \)[/tex].

We are given:
- [tex]\( \mu_X = \$60 \)[/tex]
- [tex]\( \mu_Y = \$35 \)[/tex]

The mean of the sum [tex]\( S = X + Y \)[/tex] can be calculated by summing the individual means:
[tex]\[ \mu_S = \mu_X + \mu_Y \][/tex]

Substituting the given values:
[tex]\[ \mu_S = 60 + 35 \][/tex]
[tex]\[ \mu_S = 95 \][/tex]

Therefore, the mean of JT's total weekly earnings from both jobs is \[tex]$95. Next, we interpret this result in the context of the problem. Among the given options, the correct interpretation of the mean is: \[ \mu_5 = 95; JT can expect to earn \$[/tex] 95, on average, in a typical week. \]

This interpretation correctly describes the mean as an expected average earnings per week, rather than a guaranteed amount for a specific upcoming week.

So, the correct answer choice is:
[tex]\[ \mu_5=95; JT can expect to earn \$ 95, on average, in a typical week. \][/tex]

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