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Problem 3. a Department Store Has Determined That 25% of All Their Sales Are Credit Sales. a Random Sample of 75 Sales I

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Problem 3. a Department Store Has Determined That 25% of All Their Sales Are Credit Sales. a Random Sample of 75 Sales I Powered By Docstoc
					Problem 1. A department store has determined that 25% of all their sales are
credit sales. A random sample of 75 sales is selected.

a. What is the probability that the sample proportion will be
   greater than 0.34?
b. What is the probability that the sample proportion will be
   between 0.196 and 0.354?
c. What is the probability that the sample proportion will be less
   than 0.25?
d. What is the probability that the sample proportion will be less
   than 0.10?

                                                                           Answers:
                                                                      a.     0.0359
                                                                      b.     0.8411
                                                                      c.     0.5
                                                                      d.     0.0014




Problem 2. A bank has kept records of the checking balances of its customers
and determined that the average daily balance of its customers is $300 with a
standard deviation of $48. A random sample of 144 checking accounts is
selected.

a. What is the probability that the sample mean will be more than
   $306.60?
b. What is the probability that the sample mean will be less than
   $308?
c. What is the probability that the sample mean will be between
   $302 and $308?
d. What is the probability that the sample mean will be at least
   $296?

                                                                           Answers:
                                                                      a.     0.0495
                                                                      b.     0.9772
                                                                      c.     0.2857
                                                                      d.     0.8413
Problem 3. The weights of the contents of cans of tomato sauce produced by a
company are normally distributed with a mean of 8 ounces and a standard
deviation of 0.2 ounces.

a. What percentage of all cans produced contain more than 8.4
   ounces of tomato paste?
b. What percentage of all cans produced contain less than 7.8
   ounces?
c. What percentage of cans contains between 7.4 and 8.2
   ounces?
d. Ninety-five percent of cans will contain at least how many
   ounces?
e. What percentage of cans contains between 8.2 and 8.4
   ounces?

                                                                           Answers:
                                                                      a.      2.28%
                                                                      b.     15.87%
                                                                      c.     97.58%
                                                                      d.    7.671 oz
                                                                      e.     13.59%




Problem 4. There are 8,000 students at the University of Tennessee at
Chattanooga. The average age of all the students is 24 years with a standard
deviation of 9 years. A random sample of 36 students is selected.

a. Determine the standard error of the mean.
b. What is the probability that the sample mean will be larger than
   19.5?
c. What is the probability that the sample mean will be between
   25.5 and 27 years?

                                                                         Answers:
                                                                      a.   1.5
                                                                      b.   0.9986
                                                                      c.   0.1359
Problem 5. The weights of items produced by a company are normally
distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces.

a. What is the probability that a randomly selected item from the
   production will weigh at least 4.14 ounces?
b. What percentage of the items weigh between 4.8 to 5.04
   ounces?
c. Determine the minimum weight of the heaviest 5% of all items
   produced.
d. If 27,875 of the items of the entire production weigh at least
   5.01 ounces, how many items have been produced?


                                                                         Answers:
                                                                      a.   0.8849
                                                                      b. 12.28%
                                                                      c.    4.992
                                                                      d. 625,000

				
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