# Project #4394 - Statistics

1.)  A box contains four pennies, three dimes, two quarters, and one half dollar.  Construct the probability distribution letting x be the amount of cents for each coin

(i.e.  5, 10, … )                       x    P(x)

Now find the mean and standard deviation to 2 decimal places.

Mean:                                                                          _______________________

Standard Deviation:                                                    _______________________

(sections 5.1, 5.2)

2.)  (section 5.3)  According to Harper’s Index, 50% of all federal inmates are serving time for drug dealing.  A random sample of 16 inmates is selected.

a.)     What is the probability that 12 or more are serving time for drug dealing?

b.)    What is the probability that 7 or fewer are serving time for drug dealing?

c.)    What is the probability that between 9 and 13 inclusively are serving time for drug dealing?

d.)   What is the probability that half of them are serving time for drug dealing?

3.)       (section 5.3)  Referring back to problem 2, find the expected number of inmates serving time for drug dealing.  What is the standard deviation?  State answers to 2 decimal places.

4.) (section 5.1)   The probabilities of a machine manufacturing 0, 1, 2, 3, 4 or 5 defective parts in a day are 0.68, 0.19, 0.09, 0.025, 0.01 and x.

a.)  Set up a probability distribution table and find the probability of 5 defective parts.

b.)  Find  P( at least 2 defective parts)                                    _______________________

c.)  Find P (no more than 3 defective parts)                           _______________________

d.)  Find P(between 1 and 4 inclusively parts)                       _______________________

Chapter 6:

1.)  The time that it takes a randomly selected employee to perform a certain task is approximately normally distributed with a mean value of 115 seconds and a standard deviation of 15 seconds.  The slowest 12% (that is, the 12% with the longest times) are to be given remedial training.  What times qualify for the remedial training?

(Hint:  Draw a picture!! Refer to example 6-9)

___________________________

2.)  Express Courier Service has found that the delivery time for packages is normally distributed with mean 16 hours and a standard deviation of 3.25 hours.  (similar to example 6-6 & 6-7)

a.)  For a package selected at random, what is the probability that it will be delivered in 20 hours or less?  (4 decimals)

__________________

b.)  For a package selected at random, what is the probability that it will be delivered between 14.9 and 17.3 hours?  (4 decimals)

__________________

c.)  What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time?  (nearest tenth)

_________________

3.)  On the GRE in economics, scores are normally distributed with a mean of 712 and a standard deviation of 87.  If a college admissions office requires scores above the 82nd  percentile, find the cutoff point. (similar to example 6-9)

__________________

4.)  Find the standard deviation when the mean is 100 and 2.68% of the area lies to the right of 105.  (need to use the formula for st dev    st dev = (x – mean) / z score

______2.59____________

5.)   A survey found that the American family generates an average of 17.2 pounds of glass garage each year.  Assume the standard deviation of the distribution is 2.5 pounds.  find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds.  (Hint:  Use the Central Limit Theorem. Section 6.3 Why??)                    __________________

 Subject Mathematics Due By (Pacific Time) 04/15/2013 10:00 pm
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