Question

in a random sample of 36 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 50 ​months, with a standard deviation of 5 months. construct and interpret a 90 ​% confidence interval for the mean length of sentencing for this crime.

Answer 1

The answer is 90% of the crime is between 48.63 and 51.37

How to solve for the confidence interval

The sd = 5 months

n = 36

Mean length = 50

1- 0.90

= 0.1

Critical value = alpha/2 = 1.645

Margin of error

E = 1.645 x 5/√36

= 1.37

The upper and lower limits are

50 -  1.37 + 50 + 1.37

= (48.63, 51.37)

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