Question 1206771: A high school baseball player has a 0.178 batting average. In one game, he gets 5 at bats. What is the probability he will get at least 2 hits in the game? Round to four decimal places.
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
A high school baseball player has a 0.178 batting average.
In one game, he gets 5 at bats. What is the probability he will get at least 2 hits in the game?
Round to four decimal places.
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This problem is on the Binomial distribution.
The number of trials is 5. The probability of success for each individual trial is 0.178.
They want you find the probability that at least 2 trials are successful.
P = P(2) + P(3) + P(4) + P(5).
+-----------------------------------------------------------------------+
| You can calculate each of the four terms/addends above separately |
| and then add them. |
| But the shortest way is to calculate P as P = 1 - (P(0) + P(1)). |
| The sum in parentheses is a cumulative sum, and there are special |
| tools to calculate cumulative sums. |
+-----------------------------------------------------------------------+
To find the cumulative sum in parentheses, use the standard function binomcdf
of a regular calculator TI-83/84
k n p <<<---=== formatting pattern
P' = binomcdf(1, 5, 0.178)
You get for P' = 0.781611662.
Then P = 1 - P' = 1 - 0.781611662 = 0.218388338. Notice that P' is the complementary probability to P.
Rounded to 4 decimal places, the ANSWER is 0.2184.
Alternatively, to calculate cumulative distribution, you may use the Excel standard function BINOM.DIST.
Another alternative is to use free of charge online calculator
https://stattrek.com/online-calculator/binomial.aspx
This calculator is the best, since it gives an output in all formats.
Solved.
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