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(Created page with "'''Solution: A''' The probability that the digit 3 appears as a random digit is 1/10, and the number of digits equalling 3 among 10,000 random digits is approximately normally distributed with mean 10,000 * 1/10 = 1,000 and variance 10,000 * 0.1 * 0.9 = 900. Hence the probaility that we observe the digit 3 more than 931 times is approximately equal to the probability that a standard normal variable exceeds 31/30 and this is approximately equal to 0.1507.") |
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'''Solution: | '''Solution: E''' | ||
The probability that the digit 3 appears as a random digit is 1/10, and the number of digits equalling 3 among 10,000 random digits is approximately normally distributed with mean 10,000 * 1/10 = 1,000 and variance 10,000 * 0.1 * 0.9 = 900. Hence the probaility that we observe the digit 3 more than 931 times is approximately equal to the probability that a standard normal variable exceeds | The probability that the digit 3 appears as a random digit is 1/10, and the number of digits equalling 3 among 10,000 random digits is approximately normally distributed with mean 10,000 * 1/10 = 1,000 and variance 10,000 * 0.1 * 0.9 = 900. Hence the probaility that we observe the digit 3 more than 931 times is approximately equal to the probability that a standard normal variable exceeds -69/30 = -2.3 and this is approximately equal to 0.9893. | ||
Latest revision as of 03:14, 27 June 2024
Solution: E
The probability that the digit 3 appears as a random digit is 1/10, and the number of digits equalling 3 among 10,000 random digits is approximately normally distributed with mean 10,000 * 1/10 = 1,000 and variance 10,000 * 0.1 * 0.9 = 900. Hence the probaility that we observe the digit 3 more than 931 times is approximately equal to the probability that a standard normal variable exceeds -69/30 = -2.3 and this is approximately equal to 0.9893.