约翰拥有一家清洁办公楼的清洁公司。 2020 年，他公司的员工人数及其薪水如下： 11 名杂工，每人年薪 $45 936。 272 名清洁工，每人时薪$ 5.20，每天工作 8 小时，每月共工作 20 天。
12 名主管，男女比例为 1 : 3，每人月薪比清洁工的月薪高 235%。
11 名司机，每人每周薪水 $594.50，每月按 4 周计算。此外，雇主和雇员都必须将雇员月薪的一部分缴纳给中央公积金（CPF）。
表格显示了新加坡公民的 CPF 缴纳比例和分配比例。

(a)
2020 年每名杂工的年薪比 2017 年多 2.5%。
求 2017 年每名杂工的年薪。
(b)
李女士是一名 65 的新加坡公民，在约翰的清洁公司担任清洁工。计算 2020 年每月存入李女士 CPF 账户的缴存总额。
(c)
约翰每月会从所有员工中随机抽取一名“本月优秀员工”。

陈先生评论说，随机抽中一名男主管作为本月优秀员工的概率是极不可能的。
你同意陈先生的评论吗？请说明你的理由。
(d)
约翰声称，薪水最低的员工的薪水与所有员工平均薪水之间的差额占所有员工平均薪水的百分比小于 25%。
请写出所有计算步骤，验证他的说法是否正确。

逆百分数问题百分比增减单一事件概率表示为百分数计算器使用有理数比可能性度量统计图表分析与解读数系与四则运算集中趋势百分数比较 English

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完整解法

10(a)

1. Express the 2020 salary as a percentage of the 2017 salary.

Since the 2020 salary is $2.5\%$ more than the 2017 salary,

$\text{2020 salary} = 100\% + 2.5\% = 102.5\% \text{ of 2017 salary}.$

2. Find the 2017 salary by dividing by the percentage multiplier.

Let the 2017 salary be $x$ .

$102.5\% \times x = 45\,936$

$1.025x = 45\,936$

$x = \frac{45\,936}{1.025} = 44\,816$

答案

The yearly salary of each handyman in 2017 was $44 816.

10(b)

1. Find Mdm Lee's monthly salary as a cleaner.

Cleaner monthly salary
$= \$5.20 \times 8 \times 20 = \$832$

2. Use the CPF rates for age 65 and calculate the total CPF contribution.

For age 65, use the rates for above 60 to 65:

Employer contribution $= 9\%$ , employee contribution $= 7.5\%$ .

Total contribution rate
$= 9\% + 7.5\% = 16.5\%$

Total monthly CPF contribution
$= 16.5\% \times 832$
$= 0.165 \times 832 = \$137.28$

答案

The total monthly CPF contribution is $137.28.

10(c)

1. Find the number of male supervisors and the total number of employees.

Supervisors are men and women in the ratio $1:3$ .

Total parts $=1+3=4$ .

Number of male supervisors
$=\frac{1}{4}\times 12=3.$

Total number of employees
$=11+272+12+11=306.$

2. Calculate the probability and justify the comment.

Probability of selecting a male supervisor
$=\frac{3}{306}=\frac{1}{102}\approx 0.0098=0.98\%.$

This probability is very small, so the event is most unlikely.

答案

Yes. There are $3$ male supervisors out of $306$ employees, so the probability is $\dfrac{3}{306}=\dfrac{1}{102}\approx 0.98\%$ , which is very small. Hence it is most unlikely.

10(d)

1. Find the monthly salary for each type of employee.

Cleaner’s monthly salary:
$5.20 \times 8 \times 20 = \char36{}832$

Handyman’s monthly salary:
$\dfrac{45936}{12}=\char36{}3828$

Supervisor’s monthly salary:
$832 \times 335\% = 832 \times 3.35 = \char36{}2787.20$

Driver’s monthly salary:
$594.50 \times 4 = \char36{}2378$

2. Find the total monthly salary paid to all employees.

Total monthly salary
$=11(3828)+272(832)+12(2787.20)+11(2378)$
$=42108+226304+33446.40+26158$
$=\$328016.40$

3. Find the mean monthly salary of all employees.

Total number of employees:
$11+272+12+11=306$

Mean monthly salary:
$\dfrac{328016.40}{306}=\$1071.95\text{ approximately}$

4. Express the difference between the lowest salary and the mean salary as a percentage of the mean salary, then verify the statement.

The lowest paid employees are the cleaners, with monthly salary $\char36{}832$ .

Difference:
$1071.95-832=\$239.95$

Percentage of the mean salary:
$\dfrac{239.95}{1071.95}\times 100\%=22.4\%\text{ approximately}$

Since $22.4\%<25\%$ , John’s statement is valid.

答案

The percentage difference is approximately $22.4\%$ , which is less than $25\%$ . Therefore, John’s statement is valid.

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完整解法

10(a)

10(b)

10(c)

10(d)

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