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,
_{}