Advertisements
Advertisements
Question
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. What percent of people earn between $45,000 and $65,000?
Advertisements
Solution
Let x denotes the annual salaries of employees in a large company
Mean µ = 50,000 and S.D σ = 20,000
Standard normal variate z = `(x - mu)/sigma`
P(people ear between $45,000 and $65,000)
P(45000 < x < 65000)
When x = 45,000
z = `(45, 000 - 50, 000)/(20, 000)`
= `(-5000)/(20, 000)`
= `(-1)/4`
z = – 0.25
When x = 65,000
z = `(5, 000 - 50, 000)/(20,000)`
= `(15000)/(20, 000)`
= `3/4`
z = 0.75
P(45000 < x < 65000) = P(– 0.25 < z < 0.75)
= P(– 0.25 < z < 0) + P(0 < z < 0.75)
= p(0 < z < 0.25) + P(0 < z < 0.75)
= P(0 < z < 0.25) + P(0 < z < 0.75)
= 0.0987 + 0.2734
= 0.3721
P(45000 < x < 65000) in percentage
= 0.3721 × 100
= 37.21
APPEARS IN
RELATED QUESTIONS
Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 3 will have a laptop?
The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e–2.8 = 0.06]
In a test on 2,000 electric bulbs, it was found that bulbs of a particular make, was normally distributed with an average life of 2,040 hours and standard deviation of 60 hours. Estimate the number of bulbs likely to burn for more than 2,150 hours
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height greater than 72 inches
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints
Choose the correct alternative:
If X ~ N(µ, σ2), the maximum probability at the point of inflexion of normal distribution
Choose the correct alternative:
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:
Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time. Between 20 and 22 hours?
