A waitress believes the distribution of her tips has a model that is slightly skewed to the left, with a mean of $9.40 and a standard deviation of $6.10. She usually waits on about 60 parties over a weekend of work.

a) Estimate the probability that she will earn at least $600

P(tips from 60 parties > $600)

b) How much does she earn on the best 5% of such weekends?

The total amount that she earns on the best 5% of such weekends is at least $__

a. P(tips from 60 parties > $600)=0.461

b. The total amount that she earns on the best 5% of such weekends is at least $19.43.

Step-by-step explanation:

a. To earn $600 in 60 parties means $10 per party in average.

If we assume a normal distribution of tips, we can calculate the z-value and its probability for this situation:

There is a probability of 46% that she earns at least $600 over a weekend of work.

b. The best 5% of the weekends corresponds to:

This probability (5%) corresponds to a z-value of z=1.6449.

In tips, this value represents:

The total amount that she earns on the best 5% of such weekends is at least $19.43.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)