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. A) How many people paid between $10,000 and $11,000 B) How many paid less than $10,000 C) How many paid more than $12,000

A) 6827 people

B) 1587 people

C) 1620 people

Step-by-step 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