Examination of court records in a particular state shows that the mean sentence length for first-offense drug dealers is 26 months with a standard deviation of 2 months. the records show that the sentence lengths are normally distributed. 1) what is the z score for a 23 month sentence length? what is the probability of getting a sentence below that? 2) a defense attorney is concerned that his client's sentence was unusually harsh at 30 months. what percent of sentences are 30 months or longer? calculate the z score and report the area. 3) would you consider a 30 month sentence harsh? explain

Answer and explanation:

Given : Examination of court records in a particular state shows that the mean sentence length for first-offense drug dealers is 26 months with a standard deviation of 2 months. The records show that the sentence lengths are normally distributed.

i.e. Mean , Standard deviation

Using Z-score formula,

1) What is the Z score for a 23 month sentence length? What is the probability of getting a sentence below that?

The Z score value for a is given by,

The probability of getting a sentence below that is

i.e.

2) A defense attorney is concerned that his client's sentence was unusually harsh at 30 months. What percent of sentences are 30 months or longer? Calculate the Z score and report the area.

The Z score value for a is given by,

The probability of getting a sentence below that is

i.e.

Into percentage,

3) Would you consider a 30 month sentence harsh? Explain

Since the percentage for 30 months or greater is harsh because the smaller value of percentage of