At basketball practice you made 21 out of 80 shots.
2 answers:
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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>
Problem 1
<h3>Answer: 6.7</h3>----------------
Work Shown:
The two points are and
Apply the distance formula to get the following
The distance between the two endpoints is roughly 6.7 units. This is the same as saying the segment is roughly 6.7 units long.
======================================================
Problem 2
<h3>Answer: 3.6</h3>----------------
Work Shown:
We'll use the distance formula here as well.
This time we have the two points and
The distance between them is...
This distance is approximate.