Answer:
<u>A. Mean of the amount Sally spends on breakfast daily = $ 3.90</u>
<u>Standard deviation of the amount Sally spends on breakfast daily = $ 0.34 (rounding to the next cent)</u>
<u>B. Mean of the amount Sally spends on breakfast weekly = $ 27.30</u>
<u>Standard deviation of the amount Sally spends on breakfast weekly = $ 0.89 (rounding to the next cent)</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Average price of a cup of coffee = $ 1.40
Standard deviation = $0.30
Average price of a muffin = $ 2.50
Standard deviation = $ 0.15
The two prices are independent of each other
2. What is the mean and standard deviation of the amount Sally spends on breakfast daily?
Let's recall that:
1. The mean of the sum of two independent variables is the sum of their means.
2. The variance of the sum of two independent variables is equal to the sum of their variances.
Therefore,
Mean of the amount Sally spends on breakfast daily = Average price of a cup of coffee + Average price of a muffin
Replacing with the values we know:
Mean of the amount Sally spends on breakfast daily = 1.40 + 2.50
Mean of the amount Sally spends on breakfast daily = $ 3.90
Variance of the amount Sally spends on breakfast daily = Variance of the price of a cup of coffee + Variance of the price of a muffin
Replacing with the values we know:
Variance of the amount Sally spends on breakfast daily = 0.30² + 0.15²
Variance of the amount Sally spends on breakfast daily = 0.1125
Standard deviation of the amount Sally spends on breakfast daily = √0.1125
Standard deviation of the amount Sally spends on breakfast daily = $ 0.34 (rounding to the next cent)
3. What is the mean and standard deviation of the amount she spends on breakfast weekly (7 days)?
Mean of the amount Sally spends on breakfast weekly = 7 * Mean of the amount Sally spends on breakfast daily
Mean of the amount Sally spends on breakfast weekly = 7 * 3.90
Mean of the amount Sally spends on breakfast weekly = $ 27.30
Variance of the amount Sally spends on breakfast weekly = 7 * Variance of the amount Sally spends on breakfast daily
Variance of the amount Sally spends on breakfast weekly = 7 * 0.1125
Variance of the amount Sally spends on breakfast weekly = 0.7875
Standard deviation of the amount Sally spends on breakfast weekly = √0.7875
Standard deviation of the amount Sally spends on breakfast weekly = $ 0.89 (rounding to the next cent)
