1)The driver of a truck loaded with 900 boxes of books will be fined if the total weight of the boxes exceeds 36450 pound. If the distribution of the weight of a box has a mean of 40 pounds and a variance of 36, find the approximate probability that the driver will be fined.
2) "How would you describe your own physical health at this time? Would you say physical health is-excellent, good, only fair, or poor?" The Gallup Poll asked this question of 1005 randomly selected adults, of whom 29% said "excellent." Suppose that in fact the proportion of the adult population who say their health is excellent is 0.29. What is the probability that the sample proportion of an SRS of size 1000 who say their health is excellent lies between 26% and 32%?
3) Suppose it can be assumed that 60 percent of adults favor capital punishment. Find the probability that on a jury of twelve members:
a) All will favor capital punishment.
b) There will be a tie.
4) When fifteen vehicles were observed at random for their speeds (in M.P.H.) on a freeway, the following data were obtained.
61 53 57 55 62 58 60 54 62 60 59 66 55 54 63
Suppose that from past experience it may be assumed that vehicle speed is normally distributed with standard deviation of 3.96. Construct a 93 percent confidence interval for the true mean speed.
5) A study on the amount of dye needed to get the best color for a certain type of fabric was conducted. The following data give the photometer readings for the color density of the fabric when the amount of dye used was 1% of the weight of the fabric.
13.2 11.5 12.9 13.0 11.7 10.4 12.1 12.1 11.5 10.3 11.7 12.3 11.2
Do the data demonstrate that the true mean photometer reading for the color density is significantly different from 12 at 3 percent level of significance?