SOLUTION: Shorty’s Muffler advertises it can install a new muffler in 30 minutes or less. However, the work standards department at corporate headquarters recently conducted a study and f

Question 1166765: Shorty’s Muffler advertises it can install a new muffler in 30 minutes or less. However, the work standards department at corporate headquarters recently conducted a study and found that 20% of the mufflers were not installed in 30 minutes or less. The Maumee branch installed 50 mufflers last month. If the corporate report is correct:
a. How many of the installations at the Maumee branch would you expect to take more than 30 minutes?
b. What is the likelihood that fewer than 8 installations took more than 30 minutes?
c. What is the likelihood that 8 or fewer installations too more than 30 minutes?
d. What is the likelihood that exactly 8 of the 50 installations took more than 30 minutes?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is a binomial with n=50 and p=0.20 (failure)
would expect 10 (50*).20 to have taken more than 30 minutes.
exactly 8 taking more is 50C8*0.20^8*0.80^42 or probability 0.1169
fewer than 8 would be <= 7 and that probability would be 0.1904
calc binompdf(50,0.2.8) for the first
binomcdf (50,0.2,7) for the second.
normal approximation mean is 10
variance is 10*0.8 or 8
sd is sqrt(8) or 2.828
less than 8 would be z<(7.5-10)/2.828 or -0.88 and that probability is 0.1894, a decent estimate.
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