Question

Each sweat shop worker at a computer factory can put together 4.9 computers per hour on average with a standard deviation of 0.7 computers. 18 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.

1. Find the probability that a 18 person shift will put together between 84.6 and 88.2 computers per hour.
2. For part e) and f), is the assumption of normal necessary? YesNo
3. A sticker that says "Great Dedication" will be given to the groups of 18 workers who have the top 10% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

Answer 1

Answer:

Given,

Mean = nu

= 4.9*18

= 88.2

Standard deviation = sqrt(n) * s

= sqrt(18) * 0.7

= 2.97

a)

P(84.6 < X < 88.2) = P((84.6 - 88.2)/2.97 < (x-u)/s < (88.2 - 88.2)/2.97)

= P(-1.21 < z < 0)

= P(z < 0) - P(z < - 1.21)

= 0.5 - 0.1131394 [since from z table]

= 0.3869

b)

No

c)

Here for 90th percentile 1.28

Consider,

x = mean + z*standard deviation

= 88.2 + 1.28*2.97

= 88.2 + 3.8016

= 92.0016