3. The manager of a local soft drink bottling Company believes that when a new beverage-

dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount x at random

anywhere between 6.5 and 7.5 ounces inclusive. Suppose x has a uniform probability

distribution.

Required:

a. Graph the frequency function for x, the amount of beverage the Manager believes is

dispensed by the new machine when it is set to dispense 7 ounces.

b. Find the mean and standard deviation for the distribution graphed in part b, and locate the

mean and the interval 2 on the graph

c. Find p(x 7)

d. Find P(6.5 x 7.25)

4. An advertisement for Toyota Supra model lists the following performance specifications:

standing start, 0-50 miles per hour in an average of 5.27 seconds; braking, 60 miles per hour to 0

in 3.15 seconds on the average. An independent testing service hired by a competing

manufacturer of high-performance automobiles wants to prove that Toyota's claim are

exaggerated. A random sample of 100 trial runs gives the following results: standing start, 0-50

miles per hour in an average of x (X-bar) = 5.8 seconds and s = 1.9 seconds; braking, 60 miles

per hour to 0 in an average of x (X-bar) = 3.21 seconds and s = 0.6 second. Carry out the two

hypothesis tests, state the p-value of each test, and state your conclusions.

5. An investment analyst collects data on stock and notes whether or not dividends were paid and

whether or not the stocks increased in price over a given period. Data are presented in the

following table.

Price increaseNo Price IncreaseTotal

Dividends paid3478 112

No Dividends paid8549 134

Total 119127 246

Required:

What is the probability that a randomly selected stock was worth holding during the period in

question: That is, what is the probability that it increased in price or paid dividends or did both?