1. Suppose a box contains 10000 balls of which 3000 are red, 6000 are blue and 1000 are white. If 10 balls are randomly drawn find the probability that their are? Assume independence. Hint: first calculate probabilities for each color.
    1. 5 red balls
    2. more then 7 colored balls(blue or red)
    3. at most 3 reds
    4. no whites
  2. Suppose X is normally distributed with mean = 32 and sd = 7. Find prob:

a.       P( 16 < X < 36 )

b.      if P( X > c ) = .7578, find c

c.       if P( -c < Z < +c ) = .8582, find c

  1. The amount of cereal filled by a machine is normally distributed and has a mean of 18 oz. and sd of 0.15 oz. Find the probability of a cereal box containing less then 18.25 oz
  2. A hard drive manufacturer knows that their current model is normal with a MTBF (mean time between failure) of 75 months and standard deviation of 13 months.If this manufacturer wants to have at most 8% of the drives to be returned before failure what should the guarantee be in months.
  3. If 68% of all students who take statistics pass, what is the probability that among 400 students who take statistics more then 370 will pass the course?
  4. Given the population { 16, 12, 8, 6, 4 }

.        Find population mean and var

a.       Find the mean and var of the sampling distribution of n=2 ( without replacement )

b.      Show that the formulas on page 343 hold

  1. A warden claims the average number of escapes per year for his prison is 5 with a sd of 1.5. If this claim is valid what is the approx. probability that over the next 100 years there will be less then 4 escapes per year.

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