Question

# In a random sample of 37 criminals convicted of a certain​ crime, it was determined that...

In a random sample of 37 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 57 ​months, with a standard deviation of 12 months. Construct and interpret a 90​% confidence interval for the mean length of sentencing for this crime. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Use ascending order. Round to one decimal place as​ needed.)

A. There is a 90​% probability that the mean length of sentencing for the crime is between nothing and nothing months.

B.We can be 90​% confident that the mean length of sentencing for the crime is between nothing and nothing months.

C.90​% of the sentences for the crime are between nothing and nothing months.

 sample mean 'x̄= 57 sample size    n= 37 std deviation s= 12 std error ='sx=s/√n=12/√37= 1.9728
 for 90% CI; and 36 df, value of t= 1.6883 margin of error E=t*std error    = 3.3307 lower bound=sample mean-E = 53.669 Upper bound=sample mean+E = 60.331 from above 90% confidence interval for population mean =(53.7<μ<60.3)

B.We can be 90​% confident that the mean length of sentencing for the crime is between 53.7 and 60.3 months.