Question

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.

- 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*. to find answer. - 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. to find answer* - 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 two decimal places.*

Answer #1

Given,

sample n = 555

p = 54% = 0.54

q = 1 - 0.54 = 0.46

Mean = np = 555*0.54 = 299.7

Standard deviation = sqrt(npq) = sqrt(555*0.54*0.46) = 11.74

a)

P(X >= 338) = P((x-u)/s > (338 - 299.7)/11.74)

= P(z > 3.26)

**=** 0.000557 [since from z table]

= 0.0006

= 0.06%

b)

P(X >= 285) = P((x-u)/s > (285 - 299.7)/11.74)

= P(z > -1.25)

**=** 0.8943502 [since from z table]

= 0.8944

= 89.44%

c)

P(X < 0.48) = P((x-p)/sqrt(pq/n) < (0.48 - 0.54)/sqrt(0.54(1-0.54)/555))

= P(z < -2.84)

= 0.0022557 [since from z table]

= 0.0023

= 0.23%

In an effort to cut costs and improve profits, many U.S.
companies have been turning to outsourcing. In fact, according to
Purchasingmagazine, 54% of companies surveyed outsourced
some part of their manufacturing process in the past two to three
years. Suppose 575 of these companies are contacted.
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