Tallula’s Watch Company makes
Tallula’s Watch Company makes watchesSome the watches aredefective. The probability that a given watch is defective is0.105. The number of watches that are defective in a shipment ofwatches is described by a binomial random variable . Using thebinomial distribution , determine the probability that exactly 9watches are defective in a shipment of 28 watches . Express youranswer to six decimal places .
Answer:
Let X be the number of defective watches.
Then
with
We need to find P(X=9)
Additional information:
| X | P(X=x) |
| 0 | 0.044776 |
| 1 | 0.147085 |
| 2 | 0.232954 |
| 3 | 0.236858 |
| 4 | 0.173674 |
| 5 | 0.097801 |
| 6 | 0.043983 |
| 7 | 0.016217 |
| 8 | 0.004994 |
| 9 | 0.001302 |
| 10 | 0.000290 |
| 11 | 0.000056 |
| 12 | 0.000009 |
| 13 | 0.000001 |
| 14 | 0.000000 |
| 15 | 0.000000 |
| 16 | 0.000000 |
| 17 | 0.000000 |
| 18 | 0.000000 |
| 19 | 0.000000 |
| 20 | 0.000000 |
| 21 | 0.000000 |
| 22 | 0.000000 |
| 23 | 0.000000 |
| 24 | 0.000000 |
| 25 | 0.000000 |
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