Answer:
please see detailed answers below
Explanation:
we can work these out with z scores and use of a z-table.
formula is z = (X - υ) / σ, where X is test statistic, υ is the mean and σ is the standard deviation.
a) z = (X - υ) / σ
= (235 - 204) / 55 = 0.5636.
now go to a z-table. find +0.5 along left column. now find 0.06 on top row. look where these two meet on the table. number is 0.71226. this is area to the left of z = 0.5636. since we want to find probability of at least $235, we need area to the right.
*total area under a normal curve always = 1.
so, area to the right is 1 - 0.71226 = 0.2877 = p(at least $235).
b) z = (X - υ) / σ
= (120 - 204) / 55 = -1.527.
we find just like in part a). area for this z-score is 0.6301, to the left.
p(< $120) = 0.6301.
c) for $300:
z = (X - υ) / σ
= (300 - 204) / 55 = 1.745.
area to left is 0.95950.
for $210:
z = (X - υ) / σ
= (210 - 204) / 55 = 0.109.
area to left = 0.54380.
p($210 < Z < $300) = p($300) - p($210)
= 0.95950 - 0.54380
= 0.4157.
d) top 10% means we need z area of 0.9.
z-score for that is 1.285.
z = (X - υ) / σ
1.285 = (X - 204) / 55
X - 204 = 1.285(55) = 70.675
X = 70.675 + 204
= 274.675
so cost of 10% most expensive is $274.68 (to nearest cent).