Explain why this tractor sales scenario can be a binomial experiment.
The tractor sales scenario can be a binomial experiment since there is fixed number of trials. The outcome of every trial is either a success or a failure, since each of the trials is independent. It is also notable that the probability of success is constant in every sale. Probability of success occurs when a sales associate makes one sale of an IT-8 tractor per day assumes a binomial distribution.
Using the Tractor Successes scatter plot, construct a frequency distribution for the number of successes.
Delegate your assignment to our experts and they will do the rest.
| Number of Success | Frequency |
|
0 |
10 |
|
1 |
29 |
|
2 |
26 |
|
3 |
4 |
|
4 |
3 |
Compute the mean number of successes.
Mean number of success = ∑ ( x ⋅ f ) ∑ f
| Number of Success | Frequency | x. fx |
|
0 |
10 |
0 |
|
1 |
29 |
29 |
|
2 |
26 |
52 |
|
3 |
4 |
12 |
|
4 |
3 |
12 |
|
105 |
Mean number of success= 105
Relative frequency distribution.
Explain why the relative frequency distribution table is a probability distribution.
Relative frequency distribution table is a probability distribution since it shows the proportional of the total number observations associated with each value.
Use Excel to create a scatter plot of the probability distribution.
Using the frequency distribution, what is the tractor sales success average?
Average tractor sales success = 105* 4
= 420
The Binomial Distribution is uniquely determined by n, the number of trials, and p, the probability of “success” on each trial. Using Excel, construct the Binomial Probability Distribution for four trials, n, and probability of success, p, as the tractor sales success average in part
Number of Success |
Frequency |
x. fx |
probability of success |
|
|
0 |
10 |
0 |
0.1389 |
|
|
1 |
29 |
29 |
0.4028 |
|
|
2 |
26 |
52 |
0.3611 |
|
|
3 |
4 |
12 |
0.0556 |
|
|
4 |
3 |
12 |
0.0417 |
What is the probability of at least two successes?
Probability of at least two successes = 1-P [0 Success] – P [1 Success]
=1− (1− p) n − n ⋅ p ⋅ (1−p)n−1 =1−(1−p)n−1 ⋅ (1−p+n ⋅ p)
Using the formula for the mean of the Binomial Distribution, what is the mean number of successes in part 6 above?
According to Microsoft (n.d), the excel function for binomial distribution= BINOM.DIST(x,n,p, FALSE)
Number of Success |
Frequency |
x. fx |
probability of success |
|
|
0 |
10 |
0 |
0.1389 |
0.354750491 |
|
1 |
29 |
29 |
0.4028 |
0.34719205 |
|
2 |
26 |
52 |
0.3611 |
0.120330396 |
|
3 |
4 |
12 |
0.0556 |
9.55651E-06 |
|
4 |
3 |
12 |
0.0417 |
3.02374E-06 |
9. In Excel, create a scatter plot for the Binomial Distribution. The instructions for creating a scatter plot are in part 4 above.
References
Microsoft (n.d). BINOM.DIST function. Available at; https://support.microsoft.com/en-ie/office/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c?ui=en-us&rs=en-ie&ad=ie
