Answer:
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:
[tex]z=\frac{x-\mu}{\sigma}=\frac{10.00-9.40}{6.10}=\frac{0.60}{6.10}= 0.098\\\\P(x>10)=P(z>0.098)=0.461[/tex]
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:
[tex]P(x>x_1)=0.05[/tex]
This probability (5%) corresponds to a z-value of z=1.6449.
In tips, this value represents:
[tex]x=\mu+z*\sigma=9.40+1.6449*6.10=9.40+10.03=19.43[/tex]
The total amount that she earns on the best 5% of such weekends is at least $19.43.
