The annual salaries of employees in a large company are approximately normally distributed, with a mean of $50,000 and a standard deviation of $20,000. (a) What is the probability that an employee earns a salary greater than $100,000? The company provides free public transport to the employees that earn the lowest 10% of salaries. Less than what salary does a person have to earn to qualify for free public transport? (c) A sample of 16 employees is now taken. What is the probability that the sample mean is greater than $40,000?
Answers
Answer:
ANSWER
Let x be the annual salary of employees in a large company.
x has μ=50000,σ=20000.
We know that for given x,z=
σ
x−μ
We have to find the percent of people earning between 45,000 and 65,000
First let us find P(45000<x<65000)
For x=45000,z=
20000
45000−50000
=−0.25
and for x=65000,z=
20000
65000−50000
=0.75
∴P(45000<x<65000)=P(−0.25<z<0.75)
=P(z<0.75)−P(z<−0.25)
=0.7734−(1−0.5986) (from normal distribution table)
=0.372
∴P(45000<x<65000)=0.372=37.2%
Hence the percent of people earning between 45,000 and 65,000 is 37.2%
Step-by-step explanation:
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. a) What is the ... earns a salary greater than $100,000 b) The company provides free public transport to the employees that earn the lowest 10% of salaries.