THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The length of time it takes to be seated at a local restaurant on Friday night is normally distributed with a mean of 15 minutes and a standard deviation of 4.75 minutes.
-A fair coin is flipped 100 times.The probability of obtaining between 40 and 60 heads is approximately:
A)0.6826
B)0.7518
C)0.9544
D)0.9973

Question

Quizplus · Accepted Answer

The probability of obtaining between 40 and 60 heads in 100 flips of a fair coin can be approximated using the normal distribution because of the Central Limit Theorem. The expected number of heads (mean) is 50, with a standard deviation of $\sqrt{100 \times 0.5 \times (1-0.5)} = 5$. Using the empirical rule (68-95-99.7 rule), we find that approximately 95% of the data falls within two standard deviations of the mean, which corresponds to between 40 and 60 heads. Therefore, option C (0.9544) is the closest approximation.