Answer:
A) Molly is able to afford 60% of the motorcycles available.
B) The price at the 30th percentile is $11,920.
C) A motorcycle priced at $25,000 is an outlier because it exceeds $24,792.
Explanation:
Given data:
Mean (μ) = $14,000
Standard deviation (σ) = $4,000.
A) We calculate the standard score Z for x = $15,000 using the standard normal table (see attached figure):
Z = (x - μ) / σ
Z = (15000 - 14000) / 4000
Z = 0.25
Referring to the table, this corresponds to 60%, meaning Molly can buy 60% of the motorcycles.
B) According to the second figure, the 30th percentile Z-value is -0.52, which translates to a price of:
x = μ + Z × σ
x = 14000 + (-0.52 × 4000)
x = $11,920
C) Using the 1.5 × IQR rule, an outlier is any value larger than 1.5 times the interquartile range added to the third quartile.
The third quartile corresponds to Z = 0.6745:
x = 14000 + 0.6745 × 4000 = $16,698
The first quartile corresponds to Z = -0.6745:
x = 14000 - 0.6745 × 4000 = $11,302
Therefore,
IQR = 16698 - 11302 = $5,396
The cutoff for outliers is:
16698 + 1.5 × 5396 = $24,792