Question

The average sale price (online) for four year old Harley Davidson touring motorcycles is approximately normally distributed with a mean of $14,000 and a standard deviation of $4,000.
A) Molly has saved up $15,000 to spend on a motorcycle. What proportion of the available motorcycles of this type can she afford?




B) what is the 30th percentile for the prices of motorcycles of this type?




C) show that a motorcycle priced at $25,000 would be considered an outlier by the 1.5 x IQR rule.

Answer 1

Answer:

A) Molly can buy 60% of the available motorcycles.

B) The 30th percentile is $11920

C) $25,000 is considered an outlier because is greater than: $24792

Explanation:

Data:

mean, μ =  $14,000

standard deviation, σ = $4,000.

A) Using standard normal distribution table (see first figure attached) we have to compute Z (the standard variable) for an x = $15,000 (x is the actual variable) as follows:

Z = (x - μ)/σ

Z = (15000 - 14000)/4000

Z = 0.25

From the table, that represent 60%, that is, Molly can buy 60% of the available motorcycles.

B) From the second figure attached, we can see that 30% of the results (here, the motorcycles prices) correspond to a value of Z = -0.52. That correspond to a price of:

x = μ + Z*σ

x = 14000 + (-0.52)*4000

x = $11920

C) The 1.5 x IQR rule states that any value bigger than 1.5 times the  interquartile range (IQR) added to the third quartile is an outlier.

The third quartile is located at Z = 0.6745, in terms of the actual variable:

x = μ + Z*σ

x = 14000 + 0.6745*4000

x = $16698

The first quartile is located at Z = -0.6745, in terms of the actual variable:

x = μ + Z*σ

x = 14000 - 0.6745*4000

x = $11302

Then:

IQR = 16698 - 11302 = $5396

The third quartile value added to 1.5 x IQR is equal to 16698 + 1.5*5396 = $24792