Answer:
A. Sally's average daily expenditure on breakfast is $3.90
The standard deviation for her daily breakfast expenses is $0.34 (rounded to the nearest cent)
B. Sally's average weekly breakfast spending amounts to $27.30
The standard deviation for her weekly breakfast expenses is $0.89 (rounded to the nearest cent)
Step-by-step explanation:
1. Let's analyze the provided information to answer the question accurately:
Average cost of a cup of coffee = $1.40
Standard deviation = $0.30
Average cost of a muffin = $2.50
Standard deviation = $0.15
The prices of the two items are independent.
2. How do we calculate the mean and standard deviation of Sally's daily breakfast expenditure?
Let's remember that:
1. The mean of the total of two independent variables equals the total of their means.
2. The variance of the total of two independent variables is the sum of their variances.
Thus,Mean of Sally's daily breakfast expenditure = Average cost of coffee + Average cost of muffin
Replacing with known values:
Mean of Sally's daily breakfast expenditure = 1.40 + 2.50
Mean of Sally's daily breakfast expenditure = $3.90
Variance of Sally's daily breakfast expenditure = Variance of coffee cost + Variance of muffin cost
Replacing with known values:
Variance of Sally's daily breakfast expenditure = 0.30² + 0.15²
Variance of Sally's daily breakfast expenditure = 0.1125
The standard deviation for Sally's daily breakfast expenditure = √0.1125
The standard deviation for Sally's daily breakfast expenditure = $0.34 (rounded to the nearest cent)
3. Calculating the mean and standard deviation for Sally's weekly breakfast expenses (7 days)?
The weekly average spending on breakfast = 7 * Daily average
Weekly average breakfast expenditure = 7 * 3.90Weekly average breakfast expenditure = $27.30
Variance of Sally's weekly breakfast expenditure = 7 * Daily variance
Weekly variance for breakfast expenses = 7 * 0.1125
Weekly variance for breakfast expenses = 0.7875
The standard deviation for Sally's weekly breakfast expenses = √0.7875
Standard deviation for Sally's weekly breakfast expenses = $0.89 (rounded to the nearest cent)
