Statistics Help
1) Sam is representative who sells large appliances such as refrigerators, stoves, and so forth. Let x = number of appliances Sam sells on a given day. Let f = frequency (number of days) with which he sells x appliances. For a random sample of 240 days, Sam had the following sales record.
X 0 1 2 3 4 5 6 7
F 9 72 63 41 28 14 8 5
Assume the sales record is representative of the population of all sales days.
a) Use the relative frequency to find the p(x) for x = 0 to 7
Solution: We have the following table:
|
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
Total |
|
|
9 |
72 |
63 |
41 |
28 |
14 |
8 |
5 |
240 |
The probability is found as:
Using the previous table we obtain the probabilities as:
|
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
Total |
|
|
9 |
72 |
63 |
41 |
28 |
14 |
8 |
5 |
240 |
|
|
0.0375 |
0.3 |
0.2625 |
0.170833 |
0.116667 |
0.058333 |
0.033333 |
0.020833 |
b) Use a histogram to graph the possibility distribution of part (a)
Solution: We have the following Histogram:
2) Find the probability p(z<1.23)
Solution: We know that
,
where
denotes the cumulative standard normal distribution.
3) The length of time to complete a door assembly on a automobile factory assembly line is normally distributed with mean = 6.7 minutes and standard deviation = 2.2 minutes. For a door selected at random, what is the probability the assembly line will be
a) 5 minutes or less
Solution: Let
be the random length of time to complete a door assembly. The probability we are looking for is
b) 10 minutes or less
Solution: We need to find
c) between 5 and 10 minutes
Solution: Now we need to find
d) more then 10 minutes
Solution: Finally,
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