Question

11. A small accounting firm pays each of its five clerks S50,000, two junior accountants S100,000, and one senior accountant $150,000. (a) What is the mean salary? (b) Suppose all eight employees receive a $10,000 raise. What is the mean salary? 12. Suppose a set of temperatures measured in celsius has a mean 30 C and standard deviation 5°C. What is the mean and standard deviation of the same set of temperatures measured in fahrenheit? The relationship between fahrenheit (F) and celsius (C) is FC+32

Answer 1

Solution: 11. A small accounting firm pays each of its five clerks $50,000, two junior accountants $100,000, and one senior accountant $150,000

(a) What is the mean salary?

Answer: We are given that there are five clerks, two junior accountants and one senior accountant. Therefore there are 8 employees in a small accounting firm.

The total amount that a small accounting firm pays to its eight employees is:

Mean salary is

$\frac{600,000}{8}=75,000$

Therefore the mean salary is 75,000

(b) Suppose all eight employees receive a $10,000 raise. What is the mean salary?

Answer: If all eight employees receive a $10,000 raise, then their salary becomes.

Salary of 5 clerks $=5 \times (50000+10000)=5 \times 60000=300000$

Salary of 2 junior accountants $=2 \times (100000+10000)=2 \times 110000=220000$

Salary of senior accountant $=1 \times (150000+10000)=160000$

Now the mean salary is:

$\frac{300000+220000+160000}{8}=85000$

Therefore the mean salary after the all eight employees receive a $10,000 raise is $85,000.

12. Suppose a set of temperatures measured in celsius has a mean $30^{\cdot }$ C and standard deviation $5^{\cdot }$ C. What is the mean and standard deviation of the same set of temperatures measured in fahrenheit? The relationship between fahrenheit (F) and celsius (C) is

$F=\left ( \frac{9}{5} \right )C+32$

Answer: The mean in fahrenheit is:

$Mean=\left ( \frac{9}{5} \right )30+32$

$=54+32$

$=86$

Therefore the mean temperature in fahrenheit is $86^{\cdot }F$

The standard deviation in fahrenheit is:

$Standard-deviation=\left ( \frac{9}{5} \right )5+32$

$=9+32$

$=41$

Therefore the standard deviation in fahrenheit is $41^{\cdot }F$