Answer:
A) 6827 people
B) 1587 people
C) 1620 people
Explanation:
Normal Auto Prices A survey finds that the prices paid for six year old Ford Fusion cars are normally distributed with a mean of $10,500 and a standard deviation of 500. Consider a sample of 10,000 people who bought six year old Ford Fusions.
The formula for z score when a random number of sample is given as
z = (x-μ)/σ/√n
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
n is the number of random sample
A) How many people paid between $10,000 and $11,000
For $10,000
z = (x-μ)/σ/√n
z = 10,000 - 10,500/ 500
= -500/500
= -1
P-value from Z-Table:
P(x = 10000) = 0.15866
For $11,000
z = (x-μ)/σ/√n
z = 11,000 - 10,500/ 500
= 500/500
= 1
P-value from Z-Table:
P(x= 11000) = 0.84134
People that paid between $10,000 and $11,000
=P(x= 11000) - P(x = 10000)
= 0.84134 - 0.15866
= 0.68268
Hence, 0.68268 × 10000
= 6826.8 people
Approximately = 6827 people
B) How many paid less than $10,000
For $10,000
z = (x-μ)/σ/√n
z = 10,000 - 10,500/ 500
= -500/500
= -1
P-value from Z-Table:
P(x<10000) = 0.15866
Converting to percentage
= 0.15866 × 100 = 15.866%
The number of people paid less than $10,000 is
15.866% × 10000
1586.6 people
= 1587 people
C) How many paid more than $12,000
z = (x-μ)/σ/√n
z = 12,000 - 10,500/ 500
= 1500/500
= 3
P-value from Z-Table:
P(x<12000) = 0.99865
P(x>12000) = 1 - P(x<12000) = 0.0013499
Converting to percentage
= 0.0013499 × 100
= 0.13499%
The number of people is 10000
Hence, the number of people who paid more than 12,000 is
0.13499% × 12000
= 1619.88 people
Approximately = 1620 people