Please solve the question and give correct answer with explanation so that i can understand it
1 answer:
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Question:
The local community theater sold a total of 240 tickets for Saturday night’s performance. They sold 180 more full-price tickets than discount tickets. Which system of equations can be used to model this situation?
Answer:
Step-by-step explanation:
Given
Represent the number of full price with x and discounted price with y.
From the question:
x = 180 more than y
So:
Also, a total of 240 were sold.
So:
Hence, the equations are:
Solving further;
Substitute 180 + y for x in
Solve for 2y
Divide through by 2
Recall that:
Hence:
<em>Full Price = 210</em>
<em>Discounted = 30</em>
<em />
Answer:
(a) Probability that Y falls into the dangerous region is 0.0013.
(b) Probability that the mean Y-bar falls into the dangerous region is 0.00001.
Step-by-step explanation:
We are given that a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg, σ = 1 mg).
A dosage of 13 mg is considered dangerous.
Let Y = <u><em>dosage of the active ingredient </em></u>
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 10 mg
= standard deviation = 1 mg
(a) Probability that Y falls into the dangerous region is given by = P(Y 13 mg)
P(Y 13 mg) = P(
) = P(Z
3) = 1 - P(Z < 3)
= 1 - 0.9987 = <u>0.0013</u>
The above probability is calculated by looking at the value of x = 3 in the z table which has an area of 0.9987.
(b) We are given that a dosage of 13 mg is considered dangerous. And we sample 49 capsules at random.
Let = sample mean dosage
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = 10 mg
= standard deviation = 1 mg
n = sample of capsules = 49
So, Probability that the mean Y-bar falls into the dangerous region is given by = P(
13 mg)
P(Y 13 mg) = P(
) = P(Z
21) = 1 - P(Z < 21)
= <u>0.00001</u>