According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 27 minutes. a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be? enter the lower limit for the interval where 68% of the values would fall to enter the upper limit for the interval where 68% of the values would fall b. If the distribution of time spent on the job is approximately bell shaped, between what two times would 95% of the figures be? enter the lower limit for the interval where 95% of the values would fall to enter the upper limit for the interval where 95% of the values would fall c. If the distribution of time spent on the job is approximately bell shaped, between what two times would 99.7% of the figures be? enter the lower limit for the interval where 99.7% of the values would fall to enter the upper limit for the interval where 99.7% of the values would fall d. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 357 and 481 minutes? At least enter percentages rounded to 1 decimal place % (Round the intermediate values to 3 decimal places. Round your answer to 1 decimal place.) e. Suppose a worker spent 400 minutes on the job. What would that worker’s z score be, and what would it tell the researcher? z score = enter the z score rounded to 3 decimal places (Round your answer to 3 decimal places.) This worker is in the lower half of workers but within select the distance from the mean threetwoone standard deviation of the mean.
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!
According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 27 minutes.
a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be?
enter the lower limit for the interval where 68% of the values would fall to enter the upper limit for the interval where 68% of the values would fall
b. If the distribution of time spent on the job is approximately bell shaped, between what two times would 95% of the figures be?
enter the lower limit for the interval where 95% of the values would fall to enter the upper limit for the interval where 95% of the values would fall
c. If the distribution of time spent on the job is approximately bell shaped, between what two times would 99.7% of the figures be?
enter the lower limit for the interval where 99.7% of the values would fall to enter the upper limit for the interval where 99.7% of the values would fall
d. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 357 and 481 minutes?
At least enter percentages rounded to 1 decimal place % (Round the intermediate values to 3 decimal places. Round your answer to 1 decimal place.)
e. Suppose a worker spent 400 minutes on the job. What would that worker’s z score be, and what would it tell the researcher?
z score = enter the z score rounded to 3 decimal places (Round your answer to 3 decimal places.)
This worker is in the lower half of workers but within select the distance from the mean threetwoone standard deviation of the mean.
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