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A company that markets user assembled furniture sells a computer desk that is advertised with the claim "less than an hour to assemble"

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A company that markets user assembled furniture sells a computer desk that is advertised with the claim "less than an hour to assemble". The company through their own testing have found that the assembly times follow are normal distribution with mean and standard deviation of 77.45 and 25.87minutes 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 finishing the desk within that time?
(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, show using the formula for transforming normal random variables that the new mean time will need to be 53.455 minutes.
(d)Assume that the company improved their plans for building the furniture and achieved a mean time of 53.455 minutes. A consumer advocacy group wishes to conduct their own testing and randomly selects 10 people to assemble the desk. It is recorded whether each person is able to complete the build within an hour or not.
What type of distribution will the number of people who complete the build on time in this sample follow if the company's claim is true? Explain your reasoning.
(e) Suppose that of the 10 randomly selected people asked to assemble the desk only 4managed to complete the assembly within 1 hour.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 sufficient evidence to refute the company's claim?