1) A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 750.
a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for Standard deviation to 4 decimal places and final answer to 2 decimal places.)
Mean=
Standard deviation =
b. What is the probability that X is less than 730? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Probability=
2) According to a company's website, the top 15% of the candidates who take the entrance test will be called for an interview. You have just been called for an interview. The reported mean and standard deviation of the test scores are 71 and 7, respectively. What is the possible range for your test score if you assume that the scores are normally distributed? (Round "z" value and final answer to 2 decimal places.)
Range= and above
3) A packaging system fills boxes to an average weight of 18 ounces with a standard deviation of 0.3 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd, and 3rd quartiles of the box weight. (Round "z" value and final answer to 2 decimal places.)
1st quartile = 2nd quartile = 3rd quartile =