In an effort to cut costs and improve profits, any US companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted.
A. What is the probability percentage that 338 or more companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal places.
B. What is the probability percentage that 285 or more companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal place.
C. What is the probability percentage that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to tywo decimal places.

Answer:

Following are the solution to this question:

Step-by-step explanation:

Given:

[tex]\ Mean = 0.54 \times 555 \\[/tex]

           [tex]= 299.7[/tex]

[tex]SD = 11.74[/tex]

In point a:

[tex]\to Z = \frac{(338 - 299.7)}{11.74}[/tex]

       [tex]= \frac{(38.3)}{11.74}\\\\= 3.26[/tex]

[tex]\to P = 0.000557\\\\\to \% = 0.06 \%[/tex]

In point b:

[tex]\to Z = \frac{(285 - 299.7)}{11.74}[/tex]

       [tex]= \frac{(-14.7)}{11.74}\\\\= -1.25\\[/tex]

[tex]\to P = 0.8944\\\\\to \% = 89.44 \%[/tex]

In point c:

[tex]\to 48\% \times 555 = 266.4\\\\\to Z = \frac{(266.4 - 299.7)}{11.74}\\\\[/tex]

       [tex]= \frac{(-33.3)}{11.74}\\\\= -2.83[/tex]

[tex]\to P = 0.002256\\\\\to \% = 0.23 \%[/tex]

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