Question

In an articic in the Journaf or Managemont, Joscph Martocchio studicd and cstimated the costs ot cmploycc abscnces. Based on a samplc ot 1r6 bluo-collar workcrs, Martccchio ostimated that the mcan amcunt ot paid time lost during a thrco-month peno w as 2 days per emp o eg with a s ar ard dev a ion o 1. days Marto chio a so es r ale d tia h mear armoun o un a d ime s a urn a h в н non h pero was 0 day pet em plo ee th a l i dar de a or UE days. Suppose we randomly select a sample of 100 blue-collar workers. Based on Martocchio's estmates a What is the probability that the อ erage a o n o pa me st during a three month penod r the 100 blue collar workers will exceed 1 5 days? Round means o 1 d mal pla e standard de lations to 2 de mal p aces and p i est declmal places.) Piz 1.5) (b) What is the probability that the average amount of unpaid time lost during a three-month period for the 100 blue collar workers will exeed15 days? (Round standard deviations to 2 decimal places and probabilities to 4 decimal places.) P 15) c Supp se e andar y select a sample ถ 00 ue collar workers and suppose the sample me an an un of unpaid me st du ng tme lost has increased above the previously cstimated 1.0 days? tree month pen d a exceed 1 de s Wau it be reasonable to con ude that he mean ส mou un ac he prevousy Click to stelex:l)the probability of observing the sample is Clirk lo selec:l) if the mean is actually 1.0

For C, First option is Yes or No, second is Small or Not Small.

Answer 1

a)

$\mu$=1.2

$\sigma$x =1.1/sqrt(100)=0.11

P(X>1.5)=P(Z>(1.5-1.2)/0.11)=P(Z>2.73)=0.0032

b)

$\mu$=1.0

$\sigma$x =1.6/sqrt(100)=0.16

P(X>1.5)=P(Z>(1.5-1.0)/0.16)=P(Z>3.13)=0.0009

c)

Yes /small