Overall, the amount of work-hours involved in the festival preparation by compan
ID: 2931757 • Letter: O
Question
Overall, the amount of work-hours involved in the festival preparation by company employees is normally distributed around 150 hours with a standard deviation of 20 hours.
What’s the probability that the mean number of work-hours will be between 160 and 190?
Members that are in the 90% will receive a 20% off coupon on food court prices. What is the minimum number of involved work-hours that you should have in order to receive such discount?
The members at or below the 15%ile of number of worked-hours must attend a one-on-one meeting with their supervisor. At least how many work-hours you should have in order to not have to attend such session?
How likely (what is the probability) is it to have the number of involved work-hours below 165?
How likely (what is the probability) is it that Scarecrow (name not previously mentioned) will have his involved work-hours between 140 and 170?
What percentile does an amount of 150 work-hours rank at?
What percentile does an amount of 120 work-hours rank at?
If 49 people (49 = size of the sample) are selected randomly, what’s the likelihood that their mean number of work-hours will be within 5 of the population mean? (mean +/- 5)
What’s the probability that the mean number of work-hours will be between 160 and 190?
Members that are in the 90% will receive a 20% off coupon on food court prices. What is the minimum number of involved work-hours that you should have in order to receive such discount?
The members at or below the 15%ile of number of worked-hours must attend a one-on-one meeting with their supervisor. At least how many work-hours you should have in order to not have to attend such session?
How likely (what is the probability) is it to have the number of involved work-hours below 165?
How likely (what is the probability) is it that Scarecrow (name not previously mentioned) will have his involved work-hours between 140 and 170?
What percentile does an amount of 150 work-hours rank at?
What percentile does an amount of 120 work-hours rank at?
If 49 people (49 = size of the sample) are selected randomly, what’s the likelihood that their mean number of work-hours will be within 5 of the population mean? (mean +/- 5)
Explanation / Answer
1)
probability that the mean number of work-hours will be between 160 and 190 =P(160<X<190)
=P((160-150)/20<Z<(190-150)/20)=P(0.5<Z<2)=0.97725-0.69115 =0.2858
2)for 90th percentile ; z =1.2816
hence corresponding score =mean+z*std deviaiton =175.63
3)fo 15th percentile ; z=-1.0364
hence corresponding score =mean+z*std deviaiton =129.27 hours
4)P(X<165)=P(Z<*165-150)/20)=P(Z<0.75)=0.7734
5) probability he has his involved work-hours between 140 and 170=P(140<X<170)=P(-0.5<Z<1)
=0.8413-0.3085 =0.5328
6)
for 150 hours ;z=(x-mean)/std deviation =(150-150)20 =0 ; for which work our is at 50th percentile
for 120 hours ;z=(x-mean)/std deviation =(120-150)20 =-1.5 ; for which work our is at 6.68th percentile
7) std error of mean =std deviaiton/(n)1/2 =20/(49)1/2 =20/7
hence probability =P(|X|<mean-5) =P(-5/(20/7)<Z<5/(20/7)) =P(-1.75<Z<1.75)=0.9599-.0401 =0.9199
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