Question

A waitress believes the distribution of her tips has a model that is slightly skewed to the right​, with a mean of ​$10.60 and a standard deviation of ​$6.40. She usually waits on about 50 parties over a weekend of work. ​a) Estimate the probability that she will earn at least ​$650. ​b) How much does she earn on the best 1​% of such​ weekends

Answer 1

Let X is a random variable shows the tip. Here X has mean and SD as follows:

(a)

The sample size: n=50

Let S shows the total tip on weekends. Since sample size is greater than 30 so according to central limit theorem sampling distribution of sample sum will be approximately normal with mean and SD as follows:

The z-score for S = 650 is

The  probability that she will earn at least ​$650 is

Answer: 0.0040

b)

Here we need z-score that has 0.01 area to its right. The z-score 2.33 has 0.01 area to its right. The required S is

Answer: $635.44