Question

In a​ country, the mean time served by prisoners released from prison for the first time is 34.4 months. Assume the standard deviation of the times served is 15.3 months. Let x denote time served to first release by a prisoner. Complete parts​ (a) through​ (e) below.

a. Find the standardized version of x.

b. Find the mean and standard deviation of the standardized variable.

c. Determine the​ z-scores for prison times served of 77.9 months and 26.3 months. Round your answers to two decimal places.

d. Interpret your answers in part​ (c).

e. Construct a graph that depicts your results from parts​ (b) and​ (c).

Answer 1

Let x denote time served to first release by a prisoner.

$\mu$ = 34.4

$\sigma$ = 15.3

a) The standardised version of x

The a-score is given by Z = X-34 15.3 by The mean of a iso and the standard deviation gais I. This are the constant values a stem daderdised variable que cy The z-score for the prison time served of 77.9 month and 2 6.3 months. u=77.9 so f 2,= 77.9-34.4 = 43.5 = 2.84 15.3 15.3 F2=2.847 x =26.3 so 7 = 26.3-34.4 - -8.1 = -0.53 15.3 15.3 1:22=-0.537

Therefore the z- score for a prison time served of 77.9 months is 2.84 and the z-score for a prison time served of 26.3 months is -0.53.

d) The z-score for a prison time served of 77.9 months is 2.84 standard deviation above the mean prison time

z score for a prison time served of 26.3 months is -0.53 standard deviation below the mean prison time.

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