The ages of the patients in a doctor's surgery are: 27, 13, 16, 20, 41 and 9. Find the mean of this set of data. Another patient
1 answer:
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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>
<h2>Answer:</h2>
<em>Angle 1 measures 25 degrees</em>
<h2>Explanation:</h2>Hello! Remember you have to write complete questions in order to get good and exact answers. Here I'll assume the diagram shown below. In that figure, we know that:
The figure shows that these two angles are supplementary, so they add up to 180 degrees. Therefore: