normal distribution probability

Question 3.

A company that markets user assembled furniture sells a computer desk that is advertised

with the claim \less than an hour to assemble". However, through postpurchase 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.

(a) Using this information and assuming that desk assembly time follows the normal

probability model, show that the mean and standard deviation for the assembly time

are 77.45 and 25.87 minutes respectively.

(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 nishing the desk within that time?

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(c) Wishing to maintain the \less than an hour to assemble" claim, the company hopes

that revising the instruction and labelling 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 this action did lower the mean

assembly time but only to 55 minutes. Nevertheless, the company did achieve the

60% in an hour goal too. How was that possible?

(e) A consumer advocacy group has conducted their own test. Of the 10 people asked

to assemble the desk only 4 managed to complete the assembly within the 1 hour

period. One member of the team conducting this test says that clearly the company's

claim, that 60% of people can complete the assembly within 1 hour, is incorrect as

4 out of 10 is not 60%. Another team member is not so sure. What do you think?

Does this test provide sucient evidence to refute the company's claim? (

Hint: If

the company's claim is correct, what is the probability that of the 10 people selected,

four or less completed the assembly within the hour?)

Ok so Ive gone through my lab notes, lecture notes, even asked a fourth year student....Im at a loss. I am willing to do the working out but Ive spent at least 10 hours staring at these questions and scribbling things that come up with nothing. I need step by step instructions to work this through! please help!