Respuesta :
Answer:
a) The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
b) The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
c) The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
d) A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
Step-by-step explanation:
a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?
For college graduates in business, the salary distributes normally with mean salary of $53,901 and standard deviation of $15,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
[tex]z=\frac{x-\mu}{\sigma} =\frac{65000-53901}{15000} =0.74[/tex]
The probability is then
[tex]P(X>65,000)=P(z>0.74)=0.22965[/tex]
The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?
For college graduates in health sciences, the salary distributes normally with mean salary of $51,541 and standard deviation of $11,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
[tex]z=\frac{x-\mu}{\sigma} =\frac{65000-51541}{11000} =1.22[/tex]
The probability is then
[tex]P(X>65,000)=P(z>1.22)=0.11123[/tex]
The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
c. What is the probability that a new college graduate in health sciences will earn a starting salary less than $40,000?
To calculate the probability of earning less than $40,000, we can calculate the z-value:
[tex]z=\frac{x-\mu}{\sigma} =\frac{40000-51541}{11000} =-1.05[/tex]
The probability is then
[tex]P(X<40,000)=P(z<-1.05)=0.14686[/tex]
The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
d. How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?
The z-value for the 1% higher salaries (P>0.99) is z=2.3265.
The cut-off salary for this z-value can be calculated as:
[tex]X=\mu+z*\sigma=51,541+2.3265*11,000=51,541+25,592=77,133[/tex]
A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
