Find the probability that among 10,00 random digits the digit 3 appears not more than 931 times.

• 0.9
• 0.925
• 0.95
• 0.975
• 0.99

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 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.