Q) Please answer the following situations: (Please show work. ) A. It is desired

Question

Q) Please answer the following situations: (Please show work.)

A. It is desired to locate a control on a machine. Assume the mean person can reach 80 cm with a standard deviation of 5 cm. Where should the control be to include 97.5%?

B. Design a tote pan which 95% of the employees can lift. Assume 50% can lift 20 kg and a standard deviation is 5 kg.

C. Assume you wish to purchase an adjustable workstation (for standing work), which accommodated at least 98% of the population. What should be the range of the workstation height?

D. Assume you wish to purchase a chair, which accommodated at least 95% of the population. What should be the range of the seat height?

Explanation / Answer

(A)answer is 89.8

here we use standard normal variate z=(x-mean)/sd

we want x such that P(X<x)=0.975 (97.5%)

so first we find z such that P(Z<z)=0.975 and z=1.96 ( using ms-excel=normsinv(0.975))

now 1.96=(x-80)/5

or x=80+1.96*5=89.8

(B) here we use standard normal variate z=(x-mean)/sd

P(Z<z)=0.5 and z=0

and (20-mean)/5=0

or, mean=20

now P(Z<z)=0.95 and z=1.645

x=20+1.645*5=28.225

(C) here mean and standard deviation workstation height is needed, please provide

(D) here also meand and standard deviation of seat height is needed, please provide

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