Apsychological researcher did a study with a sample of 84 boys and found that the meam length of time that they remained engaged with a science exhibit at a museum was 107 second. assuming that from past studies it was known that the population standard deviation was 11.7a) the best estimate for the population mean u is__b) find the 99% confidence interval of mean length of time for a recent population

Sample size= n= 84
sample mean= x = 107 s
population standard deviation =σ= 11.7

As, population standard deviation is given so we use the estimate:
                             x(+/-) z(α/2)(σ/√n)

At 99% Confidence interval means significance level is α=1-0.99= 0.01
So,
α/2=0.005
Now, z at α/2=0.005 
z= 2.576
Now, by putting values 
                               107(+/-)((2.576)(11.7/√84)) 
              ( 107-((2.576)(11.7/√84)), 107+((2.576)(11.7/√84))  )    
               (103.7, 110.288)