According to a 2004 report by Roger Boe et. Al. of Correctional Service Canada, the mean...

According to a 2004 report by Roger Boe et. Al. of Correctional Service Canada, the mean length of a Canadian jail sentence in 2001/2002 was ? = 4.10 months with σ = 9.75 months.

a) Can we assume that prison sentences are normally distributed? Please explain.

b) Using the central limit theorem, what is the approximate probability that the mean sentence for a random sample of 225 prisoners is more than 4.75 months?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 4.10

standard deviation = = 9.75

n = 225

(a)

this is sampling distribution of narmal population standARD DEVIATION KNOWN

AND SAMPLE MEAN

(b)

= 4.10

= / n = 9.75 / 225 = 0.65

P( >4.75 ) = 1 - P( < 4.75)

= 1 - P[( - ) / < (4.75-4.10) /0.65 ]

= 1 - P(z <1 )

Using z table

= 1 - 0.8413

= 0.1587

probability= 0.1587

orchestra answered 1 year ago

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