In a random sample of 36 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 54 months, with a standard deviation of 13 months. Construct and interpret a 90% confi interval for the mean length of sentencing for this crime. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). Click here to view the table of critical t-values. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to one decimal place as needed.) O A. There is a 90% probability that the mean length of sentencing for the crime is between and months. O B. We can be 90% confident that the mean length of sentencing for the crime is between and months, O C. 90% of the sentences for the crime are between and months.

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!