A Premier Brand in the Kraft Foods Portfolio

1) Use the standard normal distribution to find P(-2.25 < z < 1.25).

A) .0122 B) .8821 C) .8944 D) .4878

z1 -2.25 0.4878 Formula embedded:

z2 1.25 0.3944 0.8822

2) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above...

a. What is the probability that during a randomly selected month PCE's were between $775.00 and $990.00?

A) .0421 B) .0001 C) .9999 D) .9579

900 is the µ and the σ is 50

990= 990 minus 900 divided 50 =

775= 775 minus 900 divided 50 =

P(775<z>900)=

b. What is the probability that during a randomly selected month PCE's were between $375.00 and $590.00?

A) .9579 B) .9999 C) .0001 D) .0421

375= 375 minus 900 divided 50 =

590= 590 minus 900 divided 50 =

P(775<z>900)=

c. Find the point in the distribution below which 2.5% of the PCE's fell.

A) $ 682.50 B) $ 602.00 C) $ 798.00 D) $ 17.50

Three sigma rule: 68-95-99.7 µ±2σ

Formula: $800.00

3) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 3.2 millimeters?

A) 1.5 B) 0.4571 C) 0.7111 D) 0.65

Probability = (4.5 – 3.2) / (4.5-2.5)

Probability = (1.3)/2

P= .65

4) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 12.5 gallons per minute.

a. What is the probability that at the time the machine is checked it is pumping more than 10.5 gallons per minute?

A) .50 B) .25 C) .7692 D) .667

P = (12.5-10.5)/ (12.5-8.5)

P = 2/4

P = .5

b. What is the probability that at the time the machine is checked it is pumping more than 9.0 gallons per minute?

A) .7692 B) .25 C) .50 D) .667 E) .875

µ = 10.5 gallons per minute

σ = 1.154701 gallons per minute

P= (12.5-9)/ (12.5-8.5)

P= (3.5)/4

P= .875 (Not a choice, but the correct answer)

c. What is the probability that at the time the machine is checked it is pumping more than 6.5 gallons per minute?

A) .50 B) .667 C) .7692 D) .25

P= (12.5-8.5)/ (12.5-6.5)

P= 4/6

P= .666667

5) The time between customer