Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by multiplying the number of spots showing on the one die by the number of spots showing on the other. The range of values that X can assume are the positive integers {1,2,3,4,5,6,8,9,10,12,15,16,18,20, 24,25,30,36}. Please give the corresponding probabilities for the values of X given below. Pr(X = 1) = Pr(X = 2) = Pr(X = 3) = Pr(X = 4) = Pr(X = 5) = Pr(X = 6) = Pr(X = 8) = Pr(X = 9) = Pr(X = 10) = Pr(X = 12) = Pr(X = 15) = Pr(X = 16) = Pr(X = 18) = Pr(X = 20) = Pr(X = 24) = Pr(X = 25) = Pr(X = 30) = Pr(X = 36) = Further, find the probability that X is divisible by 9.

On the first of each month, shelly runs a 5k race. she keeps track of her times to track her progress. her time in minutes is recorded in the table: jan 40.55 july 35.38 feb 41.51 aug 37.48 mar 42.01 sept 40.87 apr 38.76 oct 48.32 may 36.32 nov 41.59 june 34.28 dec 42.71 determine the difference between the mean of the data, including the outlier and excluding the outlier. round to the hundredths place. 39.98 39.22 0.76 1.21

Judy garland electronics operate on a net-profile rate of 20% on its printer cables. if the markup is $8.95 and the overhead is $4.31,find the net profit and the selling price? use the net-profit rate formula to solve this problem.

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?