Question

# In a random sample of 38 criminals convicted of a certain​ crime, it was determined that...

In a random sample of

38

criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was

55

​months, with a standard deviation of

8

months. Construct and interpret a

95​%

confidence interval for the mean length of sentencing for this crime.Click here to view the standard normal distribution table (page 1).

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

95​%

probability that the mean length of sentencing for the crime is between

nothing

and

nothing

months.

B.

95​%

of the sentences for the crime are between

nothing

and

nothing

months.

C.We can be

95%

confident that the mean length of sentencing for the crime is between

nothing

and

nothing

months.

t critical value at 0.05 significance level with 37 df = 2.026

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

55 - 2.026 * 8 / sqrt(38) < < 55 + 2.026 * 8 / sqrt(38)

52.4 < < 57.6

95% CI is (52.4 , 57.6)

We can be 95% confident that the mean length of sentencing for a crime is between 52.4 and 57.6 months.