CRJ 303 Homework 3 Name: [Show all your work (1) Assume that you have a normal d

Question

CRJ 303 Homework 3 Name: [Show all your work (1) Assume that you have a normal distribution of prior arrests wih a mean of 7 nd standard deviation of Prior Arrests for A sample of 10 people. Prison Sentences (in months) for A sample of 10 people. Person Number of Prior Armests Z-score a. Calculate Z-scores for each person in the table b. What proportion of cases have fewer than 3 prior arests? c. What proportion of cases have fewer than 5 prior arrests? d. What proportion of cases have more than 7 prior arrests? e. What proportion of cases have fewer tlhan 7 prior arrests? f What proportion of cases have more than 8 prior arrests? . What proportion of cases have more than 10 prior arrests? h. What proportion of cases have between 6 and 8 prior arrests? i. What proportion of cases have between 7 and 10 prior arrests? j. What proportion of cases have between 5 and 7 prior anrests? k. What proportion of cases have between 8 and 10 prior arrests?

Explanation / Answer

a)

Formula Z-score= (X'-mu)/(sigma/sqrt(n))

provided data mu=7,sigma=3.09,For Each observation we are calculating the z score and so here we have to take n=1 here

-1.618122977 (i.e.

(2-7)/(3.09)

(b)proportion of cases have fewer than 3 arrests= Total cases with <3 arrests/Total cases =1/10 =0.1 or 10% (the 1 case is case 1 given in the sample)

(c)proportion of cases have fewer than 5 arrests= Total cases with <5 arrests/Total cases =2/10 =0.2 or 20% (the 2 cases are case 1 &2 given in the sample)

(d)proportion of cases have more than 7 arrests= Total cases with >7 arrests/Total cases =5/10 =0.5 or 50% (the 5 cases are case 6 to 10given in the sample)

Formula Z-score= (X'-mu)/(sigma/sqrt(n))

provided data mu=7,sigma=3.09,For Each observation we are calculating the z score and so here we have to take n=1 here

Person Number of arrests Z-Score 1 2

-1.618122977 (i.e.

(2-7)/(3.09)

2 3 -1.294498382 3 5 -0.647249191 4 6 -0.323624595 5 6 -0.323624595 6 8 0.323624595 7 9 0.647249191 8 10 0.970873786 9 10 0.970873786 10 11 1.294498382

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