Each sweat shop worker at a computer factory can put together 4.9 computers per hour on average with a standard deviation of 0.9 computers. 41 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( b. What is the distribution of ? - N( c. What is the distribution of ) x? > x - N(

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Each sweat shop worker at a computer factory can put
together 4.9 computers per hour on average with a
standard deviation of 0.9 computers. 41 workers are
randomly selected to work the next shift at the factory.
Round all answers to 4 decimal places where possible and
assume a normal distribution.
a. What is the distribution of X? X ~ N(
b. What is the distribution of æ? ¤ - N(
c. What is the distribution of ) x? > x - N(
Σα Σ-Ν
d. If one randomly selected worker is observed, find
the probability that this worker will put together
between 4.7 and 4.9 computers per hour.
e. For the 41 workers, find the probability that their
average number of computers put together per hour
is between 4.7 and 4.9.
f. Find the probability that a 41 person shift will put
together between 192.7 and 200.9 computers per
hour.
g. For part e) and f), is the assumption of normal
necessary? O No
h. A sticker that says "Great Dedication" will be given to
the groups of 41 workers who have the top 15%
productivity. What is the least total number of
computers produced by a group that receives a
Yes
sticker?
minutes (round to the
nearest computer)
Transcribed Image Text:Each sweat shop worker at a computer factory can put together 4.9 computers per hour on average with a standard deviation of 0.9 computers. 41 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N( b. What is the distribution of æ? ¤ - N( c. What is the distribution of ) x? > x - N( Σα Σ-Ν d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.7 and 4.9 computers per hour. e. For the 41 workers, find the probability that their average number of computers put together per hour is between 4.7 and 4.9. f. Find the probability that a 41 person shift will put together between 192.7 and 200.9 computers per hour. g. For part e) and f), is the assumption of normal necessary? O No h. A sticker that says "Great Dedication" will be given to the groups of 41 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a Yes sticker? minutes (round to the nearest computer)
Expert Solution
Step 1

(a)

 

Determine the distribution of X.

 

The distribution of X is obtained below as follows:

Statistics homework question answer, step 1, image 1

 

Step 2

(b)

Statistics homework question answer, step 2, image 1

Thus, the value of sample mean of the sampling distribution is 4.9.

 

The value of the sampling distribution of the standard deviation is,

 

Statistics homework question answer, step 2, image 2

 

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