Answer :
To determine the more cost-effective offer for Mrs. James based on the provided probabilities and costs from each company, we need to calculate the expected yearly costs from each company. Here is a step-by-step solution:
1. Determine the fixed yearly cost for Company A:
- Company A offers a repair contract for \[tex]$12.99 per month. - The yearly cost for Company A, therefore, is \( \$[/tex]12.99 \times 12 \) = \[tex]$155.88. 2. Calculate the expected number of repairs per year: - We have the probabilities for the number of repairs as follows: - 0 repairs with probability 0.25 - 1 repair with probability 0.32 - 2 repairs with probability 0.29 - 3 repairs with probability 0.14 - The expected number of repairs (\( E \)) can be calculated as: \[ E = (0 \times 0.25) + (1 \times 0.32) + (2 \times 0.29) + (3 \times 0.14) = 1.32 \] 3. Calculate the expected yearly cost for Company B: - Company B charges \$[/tex]75 per repair with no monthly fee.
- The expected yearly cost for Company B is [tex]\( \$75 \times 1.32 \)[/tex] = \[tex]$99. 4. Compare the yearly costs from both companies: - Yearly cost from Company A: \$[/tex]155.88
- Yearly cost from Company B: \[tex]$99 Since the yearly cost from Company B (\$[/tex]99) is lower than the yearly cost from Company A (\$155.88), the offer from Company B is more cost-effective.
So, the correct answer is:
The offer from Company B is more cost-effective than the offer from Company A.
1. Determine the fixed yearly cost for Company A:
- Company A offers a repair contract for \[tex]$12.99 per month. - The yearly cost for Company A, therefore, is \( \$[/tex]12.99 \times 12 \) = \[tex]$155.88. 2. Calculate the expected number of repairs per year: - We have the probabilities for the number of repairs as follows: - 0 repairs with probability 0.25 - 1 repair with probability 0.32 - 2 repairs with probability 0.29 - 3 repairs with probability 0.14 - The expected number of repairs (\( E \)) can be calculated as: \[ E = (0 \times 0.25) + (1 \times 0.32) + (2 \times 0.29) + (3 \times 0.14) = 1.32 \] 3. Calculate the expected yearly cost for Company B: - Company B charges \$[/tex]75 per repair with no monthly fee.
- The expected yearly cost for Company B is [tex]\( \$75 \times 1.32 \)[/tex] = \[tex]$99. 4. Compare the yearly costs from both companies: - Yearly cost from Company A: \$[/tex]155.88
- Yearly cost from Company B: \[tex]$99 Since the yearly cost from Company B (\$[/tex]99) is lower than the yearly cost from Company A (\$155.88), the offer from Company B is more cost-effective.
So, the correct answer is:
The offer from Company B is more cost-effective than the offer from Company A.
