9. Examination of court records in a particular state shows that the mean sentence length for a felony conviction for robbery is 40 months with a standard deviation of 6 months. The records show that the sentence lengths are normally distributed. 1) What percentage of first-time convictions for robbery are 32 or fewer months in length? 2) A defense attorney is concerned that his client's sentence was unusually harsh at 50 months. What percent of sentences are 50 months or longer 11.Researchers need to calculate the standard error for their estimates of population parameters using sampling distributions and to compute confidence intervals. Right now, many researchers and government officials would like to know If household income has gone up or gone down (and by what amount) during the COVID year. The standard deviation of a previous population study was $6,000.00, and is to be used to calculate the standard error. Please round your responses to two decimal places. 1. If a random sample of 50 households is drawn and the head of the household is interviewed, what is the standard error for this study with n = 50? 2. 2. If the sample size were increased to 150, what would the standard error be 3. 3. If the sample size were increased to 1200, what would the standard error be? 12. f you completed Question 2, use the standard errors you calculated to compute the 95% Confidence Interval for the decline in household income for each study. 1 Study 1 with an n = 50 reported an average decrease in household income for the COVID year of $19,000.00 2. Study 2 with an n = 150 reported an average decrease in household income of $23,000.00. 3. Study 3 with an n = 1200 reported an average decrease in household income of $29,000.00. 13. Corrections officers completed a training about the management of their facilities during the COVID pandemic. The scores were distributed normally with a mean of 81 and a standard deviation of 7. Please record Z scores in two decimal places. Percentages should be shown as whole number, ex. 85 or 85%. Probabilities from the Z table should be shown as proportions in four decimal places. A percentile rank is shown as a whole number, ex. 76. 1. What is the Z score for the officer whose raw score was a 66 2. What percentage of officers scored an 81 or above? 3. What is the probability that an officer chosen at random would have a score above 75? 4. What is the Z score for an officer whose raw score was a 90? 5. What is the percentile rank for the officer whose score is a 90 6. What Z score would be needed to the in the 95th percentile - the top 7. What would the raw score be for the officer in the 95th percentile? Record this reponse as a whole number