Refer to Exercise 4.28.
a. Compute the probabilities for parts (a) − (d) if π = 3.
b. Indicate how you would compute (Py ≤ 100) for n = 1,000 and π = 3.
Exercise 4.28
In an inspection of automobiles in Los Angeles, 60% of all automobiles had emissions that do not meet EPA regulations. For a random sample of 10 automobiles, compute the following probabilities:
a. All 10 automobiles failed the inspection.
b. Exactly 6 of the 10 failed the inspection.
c. Six or more failed the inspection.
d. All 10 passed the inspection.
Use the following Minilab output to answer the questions. Note that with Minitab, the binomial probability π is denoted by p and the binomial variable y is represented by x.
Binomial Distribution with n = 10 and p = 0.6
x | P(X = x) | P(X < = x) |
0.00 | 0.0001 | 0.0001 |
1.00 | 0.0016 | 0.0017 |
2.00 | 0.0106 | 0.0123 |
3.00 | 0.0425 | 0.0548 |
4.00 | 0.1115 | 0.1662 |
5.00 | 0.2007 | 0.3669 |
6.00 | 0.2508 | 0.6177 |
7.00 | 0.2150 | 0.8327 |
8.00 | 0.1209 | 0.9536 |
9.00 | 0.0403 | 0.9940 |
10.00 | 0.0060 | 1.000 |
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