CURRENT OBJECTIVE
Create and interpret a Binomial Distribution with Technology - Excel

Question
A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a lette from A to F. Assume that each number or letter being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability.
- Round your answer to three decimal places.
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0.996
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Step 1 ：The problem is asking for the probability that at least 20 characters in the ID are numbers. This is a binomial distribution problem where the number of trials is 32 (the number of characters in the ID), the probability of success (a number being selected) is \( \frac{10}{16} \) (since there are 10 numbers and 6 letters, making 16 possible characters), and the number of successes is at least 20.

Step 2 ：We can solve this problem by calculating the cumulative probability of getting 19 or fewer numbers and then subtracting this from 1 to find the probability of getting at least 20 numbers.

Step 3 ：First, we need to calculate the cumulative probability of getting 19 or fewer numbers. This can be done using the cumulative distribution function (CDF) of the binomial distribution. Then, we subtract this from 1 to get the probability of getting at least 20 numbers.

Step 4 ：Let's write the code to solve this problem. The number of trials is 32, the probability of success is 0.625, and the cumulative probability of getting 19 or fewer numbers is 0.42191970515785016.

Step 5 ：The probability of getting at least 20 numbers is \(1 - 0.42191970515785016 = 0.578\).

Step 6 ：The final answer is \(\boxed{0.578}\).