# Question: Suppose that a particular production process fills detergent in boxes

Suppose that a particular production process fills detergent in boxes of a given size. Specifically, this process fills the boxes with an amount of detergent (in ounces) that is adequately described by a normal distribution with mean 50 and standard deviation 0.5.

a. Simulate this production process for the filling of 500 boxes of detergent. Find the mean and standard deviation of your simulated sample weights. How do your sample statistics compare to the theoretical population parameters in this case? How well do the empirical rules apply in describing the variation in the weights in your simulated detergent boxes?

b. A box of detergent is rejected by quality control personnel if it is found to contain less than 49 ounces or more than 51 ounces of detergent. Given these quality standards, what proportion of all boxes is rejected? What step(s) could the supervisor of this production process take to reduce this proportion to 1%?

a. Simulate this production process for the filling of 500 boxes of detergent. Find the mean and standard deviation of your simulated sample weights. How do your sample statistics compare to the theoretical population parameters in this case? How well do the empirical rules apply in describing the variation in the weights in your simulated detergent boxes?

b. A box of detergent is rejected by quality control personnel if it is found to contain less than 49 ounces or more than 51 ounces of detergent. Given these quality standards, what proportion of all boxes is rejected? What step(s) could the supervisor of this production process take to reduce this proportion to 1%?

**View Solution:**## Answer to relevant Questions

It is widely known that many drivers on interstate highways in the United States do not observe the posted speed limit. Assume that the actual rates of speed driven by U.S. motorists are normally distributed with mean _ mph ...In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial ...Suppose that 53% of all registered voters prefer Barack Obama to John McCain. a. In a random sample of 100 voters, what is the probability that the sample will indicate that Obama will win the election (that is, there will ...Suppose you play a game at a casino where your probability of winning each game is 0.49. On each game, you bet $10, which you either win or lose. Let P(n) be the probability that you are ahead by at least $50 after n games. ...Suppose the number of baskets scored by the Indiana University basketball team in one minute follows a Poisson distribution with λ = 1.5. In a 10-minute span of time, what is the probability that Indiana University scores ...Post your question