The average annual salary for 35 of a company’s 1200 accountants is $57,000. This describes a parameter.
1 answer:
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Given:
The formula for total cost is
where, p is the price of item and s is the sales tax rate (as a percent).
You pay $14.77 for an item priced at $14.
To find:
The the tax rate.
Solution:
You pay $14.77 for an item priced at $14. So,
Total cost (T) = $14.77
Price of item (p) = $14
Putting T=14.77 and p=14 in given formula, we get
Multiply both sides by 100.
Divide both sides by 14.
Therefore, the tax rate is 5.5%.
Answer:
(a) 0.343
(b) 0.657
(c) 0.189
(d) 0.216
(e) 0.353
Step-by-step explanation:
Let P(a vehicle passing the test) = p
Let P(a vehicle not passing the test) = q
q = 1 - p
q = 1 - 0.7 = 0.3
(a) P(all of the next three vehicles inspected pass) = P(ppp)
= 0.7 × 0.7 × 0.7
= 0.343
(b) P(at least one of the next three inspected fails) = P(qpp or qqp or pqp or pqq or ppq or qpq or qqq)
= (0.3 × 0.7 × 0.7) + (0.3 × 0.3 × 0.7) + (0.7 × 0.3 × 0.7) + (0.7 × 0.3 × 0.3) + (0.7 × 0.7 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.3)
= 0.147 + 0.063 + 0.147 + 0.063 + 0.147 + 0.063 + 0.027
= 0.657
(c) P(exactly one of the next three inspected passes) = P(pqq or qpq or qqp)
= (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)
= 0.063 + 0.063 + 0.063
= 0.189
(d) P(at most one of the next three vehicles inspected passes) = P(pqq or qpq or qqp or qqq)
= (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7) + (0.3 × 0.3 × 0.3)
= 0.063 + 0.063 + 0.063 + 0.027
= 0.216
(e) Given that at least one of the next 3 vehicles passes inspection, what is the probability that all 3 pass (a conditional probability)?
P(at least one of the next three vehicles inspected passes) = P(ppp or ppq or pqp or qpp or pqq or qpq or qqp)
= (0.7 × 0.7 × 0.7) + (0.7 × 0.7 × 0.3) + (0.7 × 0.3 × 0.7) + (0.3 × 0.7 × 0.7) + (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)
= 0.343 + 0.147 + 0.147 + 0.147 + 0.063 + 0.063 + 0.063
= 0.973
With the condition that at least one of the next 3 vehicles passes inspection, the probability that all 3 pass is,
= 0.353