Statistics - Probability and Hypothesis Testing

1. The mean life of a computer disk drive is 2,000 hours. The standard deviation is 140 hours. Assuming the life-time of the drives to be normally distributed, find the probability of a disk drive lasting more than 1,800 hours.
a. .4236
b. .9236
c. .8472
d. .5764
e. .2118
f. None of the above.

2. The yearly commissions per salesperson employed by a manufacturer of light machinery average $40,000 with a standard deviation of $5,000. What percent of the salespersons earn between $32,000 and $42,000?
a. 60.06%
b. 39.94%
c. 34.13%
d. 65.87%
e. 81.66%
f. None of the above.

3. A study of 200 stamping firms revealed these incomes after taxes:

Income After Taxes Number of Firms
Under $1 million 102
$1 million up to $20 million 61
$20 million and more 37

What is the probability that a particular firm selected has under $1 million in income after taxes?
a. 0.000
b. 0.250
c. 0.333
d. 0.510
e. None of the above.

4. A study of the opinion of designers with respect to the primary color most desirable for use in executive offices showed that:

Primary Color Number of Opinions
Red 92
Orange 86
Yellow 46
Green 91
Blue 37
Indigo 46
Violet 2

What is probability that a designer does not prefer red?
a. 1.000
b. 0.770
c. 0.000
d. 0.230
e. None of the above.

5. The manufacturer of salad dressings uses machines to dispense the dressing into bottles that move along an assembly line. The machine is working well when 8 ounces is dispensed. The standard deviation of the process is 0.15 ounce. A sample of 50 bottles is selected periodically and the assembly line is stopped when there is evidence that the average amount dispensed is less than 8 ounces. Suppose that a sample of 50 bottles reveals an average of 7.983 ounces.

1. State the null and alternative hypotheses.
2. At the .05 level of significance, is there evidence that the average amount dispensed is less than 8 ounces?

6. A machine being used for packaging raisins has been set so that, on average, 15 ounces of raisins will be packaged per box. The operations manager wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. The sample mean is 15.18 and the sample standard deviation is 0.4909. Use the t-distribution. Is there evidence that the mean weight per box is different from 15 ounces? (use level of significance equal to .05)

Please show all work so that I can understand how to work these types of problems!