Need Help with Basic Normal Model and SD

Jaskaran

Junior Member
Joined
May 5, 2006
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67
Okay, thanks for your help and input. I have a problem, that I don't know how it's done.

A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim "less than an hour to assemble." However, through post-purchase surveys the company has learned that only 25% of their customers succeeded in building the desk in under an hour; 5% said it took them over 2 hours. The company assumes that consumer assembly time follows a Normal Model.

a)Find the mean and standard deviation of the assembly time model.
Okay, so how do I find the mean? Is the mean supposedly 60 minutes...?
b)One way the company could solve this problem would be to change the advertising claim. What assembly time should the company quote in order that 60% of customers succeed in finishing the desk by then?
I don't get this one..but I'm trying to think
c)Wishing to maintain the " less than an hour" claim, the company hopes that revising the instructions and labelign the parts more clearly can improve the 1-hour success rate to 60%. If the standard deviation stays the same, what new lower mean time does the company need to achieve?
d)Months later, another postpurchase survey shows that new instructions and part labeling did lower the mean assembly time, but only to 55 Minutes. Nonetheless, the company did achieve the 60%-in-an-hour goal, too. How was that possible?

The book claims the answers are:
a)Mean 1.29 hours, SD 0.43 hours
b)1.4 hours
c).89 hours or 53.4 minutes
d)Survey results may vary, and the mean and SD may have changed.

Can ayone help me clarify, or at least, tell me what I'm missing out? Thanks.
 
Jaskaran said:
Okay, thanks for your help and input. I have a problem, that I don't know how it's done.

A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim "less than an hour to assemble." However, through post-purchase surveys the company has learned that only 25% of their customers succeeded in building the desk in under an hour; 5% said it took them over 2 hours. The company assumes that consumer assembly time follows a Normal Model.

a)Find the mean and standard deviation of the assembly time model.
Okay, so how do I find the mean? Is the mean supposedly 60 minutes...?
b)One way the company could solve this problem would be to change the advertising claim. What assembly time should the company quote in order that 60% of customers succeed in finishing the desk by then?
I don't get this one..but I'm trying to think
c)Wishing to maintain the " less than an hour" claim, the company hopes that revising the instructions and labelign the parts more clearly can improve the 1-hour success rate to 60%. If the standard deviation stays the same, what new lower mean time does the company need to achieve?
d)Months later, another postpurchase survey shows that new instructions and part labeling did lower the mean assembly time, but only to 55 Minutes. Nonetheless, the company did achieve the 60%-in-an-hour goal, too. How was that possible?

The book claims the answers are:
a)Mean 1.29 hours, SD 0.43 hours
b)1.4 hours
c).89 hours or 53.4 minutes
d)Survey results may vary, and the mean and SD may have changed.

Can ayone help me clarify, or at least, tell me what I'm missing out? Thanks.
From your questions, I have little idea of what you know about using the normal distribution. So I'll just throw out that if \(\displaystyle \L x\) is the random assembly time,

\(\displaystyle \L P( (x - \mu)/\sigma < (1 - \mu)/\sigma ) = .25\)

implies that \(\displaystyle \L (1 - \mu)/\sigma\) equals a value corresponding to .25 in the normal distribution table.

Similarly for

\(\displaystyle \L P( (x - \mu)/\sigma > (2 - \mu)/\sigma ) = .05 .\)

That gives you two equations for those two unknowns.

Same idea for the other questions.
 
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