Question

most restaurants suggest that tips should exceed 18%. suppose tips are a normally distributed random variable with a mean of 16% and a standard deviation of 3%. determine the tip amount that is exceeded only by the top 1%. (round your answer to the nearest cent.)

Answer 1

The tip amount that is exceeded only by the top 1% is approximately 23%.

Step-by-step explanation:

To determine the tip amount that is exceeded only by the top 1%, we need to find the z-score corresponding to this percentile and then use it to calculate the tip amount.

First, we calculate the z-score using the formula: z = (x - mean) / standard deviation

Next, we find the z-score that corresponds to the top 1% by looking up the value in the standard normal distribution table or using a calculator.

The z-score for the top 1% is approximately 2.33.

Finally, we use the z-score to calculate the tip amount: tip amount = mean + (z-score * standard deviation)

Plugging in the given values, the tip amount that is exceeded only by the top 1% is approximately 16% + (2.33 * 3%) = 22.99%, which rounds to 23%.