Question

A

waiterwaiter

believes the distribution of

hishis

tips has a model that is slightly skewed to the

leftleft​,

with a mean of

​$9.19.10

and a standard deviation of

​$5.15.10.

HeHe

usually waits on about

6060

parties over a weekend of work.

​a) Estimate the probability that

hehe

will earn at least

​$550550.

​b) How much does

hehe

earn on the best

55​%

of such​ weekends?

Answer 1

a) P(At least $550)

= P(Mean at least 550/60)

= P(Mean at least 9.17)

$\small = P(z \geq \frac{9.17-9.10}{5.1/\sqrt{60}})$

= P(z > 0.11)

= 0.4577

b) z score for top 5% area = 1.645

Hence,

Earnings = 9.10 + 1.645*5.1 = 17.49