Question

A local church is raising funds to purchase a new organ. The church budget includes $16,422.00 set aside for the cost of the organ, but the music committee must plan more ways to raise the additional money needed to pay for the cost of the organ, $24,545.00. Explain why the clerk should estimate when reporting the need to the church congregation, but should be accurate when writing a check to the organ company for the payment of the organ.

a) Estimation helps in quick decision-making.
b) Accuracy ensures transparency in financial transactions.
c) Estimation is more reliable for budget planning.
d) Accuracy is crucial for legal compliance.

Answer 1

Using z-scores, it is determined that the drum set is the lowest cost at -1 z-score, signaling it is the farthest below its mean cost relative to other drums. The guitar has the highest cost with a z-score of 0.25, indicating it is above the mean cost for guitars.

Step-by-step explanation:

To determine which musical instrument is the lowest and highest cost compared to other instruments of the same type, we use the concept of z-scores. The z-score tells us how many standard deviations an element is from the mean. We calculate the z-score by subtracting the mean from the observed value (the cost) and then dividing by the standard deviation. This gives us:

• For the piano: (3,000 - 4,000) / 2,500 = -0.4
• For the guitar: (550 - 500) / 200 = 0.25
• For the drum set: (600 - 700) / 100 = -1

The drum set has the lowest z-score, which means it is the farthest below the mean and hence the lowest price compared to other drums. The guitar has the highest z-score, which indicates it is above the mean and therefore has the highest price compared to other guitars. Thus, the drum set is the lowest cost and the guitar is the highest cost relative to the mean prices of those instruments.