contestada

In a random sample of 32 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 52 ​months, with a standard deviation of 9 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 ______ and ______months.B. 90​% of the sentences for the crime are between ______and _______ months.C. We can be 90​% confident that the mean length of sentencing for the crime is between ______and ______ months.

Respuesta :

dogacandu

Answer:

There is a 90​% probability that the mean length of sentencing for the crime is between 49.4 and 54.6 months.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

  • M is the sample mean length of sentencing (52 months)
  • ME is the margin of error from the mean

And margin of error (ME) from the mean can be calculated using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

  • z is the corresponding statistic of 90% confidence level (1.64)
  • s is the sample standard deviation of sentencing (9 months)
  • N is the sample size (32 criminals)

Then ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] ≈2.6

90% confidence interval for the mean length of sentencing for the crime is

52 ± 2.6 months.

Otras preguntas