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slamgirl [31]
2 years ago
11

Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a Poisson distribution with para

meter μ = 5. Use the cumulative Poisson probabilities from the Appendix Tables to compute the following probabilities. (Round your answers to three decimal places.)(a) P(X ≤ 8)(b) P(X = 8)(c) P(9 ≤ X)(d) P(5 ≤ X ≤ 8)(e) P(5 < X < 8)
Mathematics
1 answer:
kvasek [131]2 years ago
5 0

Answer:

(a) 0.932

(b) 0.0653

(c) 0.032

(d) 0.316

(e) 0.251

Step-by-step explanation:

From the table with mean parameter μ = 5, we can compute the following cumulative and density probability

(a) P(X \leq 8) = 0.932 (cumulative)

(b) P(X = 8) = 0.0653 (density)

(c) P(9 \leq X) = 1 - P(X \leq 9) = 1 - 0.968 = 0.032 (cumulative)

(d) P(5 \leq X \leq 8) = P(X \leq 8) - P(X \leq 5) = 0.932 - 0.616 = 0.316 (cumulative)

(e) P(5 < X < 8) = P(X \leq 8) - P(X \leq 5) - P(X = 8) = 0.932 - 0.616 - 0.0653 = 0.251

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Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average n
Kobotan [32]

Answer:

The test statistic value is 15.3.

Step-by-step explanation:

The hypothesis for this test is:

<em>H</em>₀: The average number of homeless people is not increasing, i.e. <em>μ</em> = 42.3.

<em>H</em>ₐ: The average number of homeless people is increasing, i.e. <em>μ</em> > 42.3.

Given:

\bar x=45.3\\\sigma=6.2\\n=1000

As the population standard deviation is provided use a single mean <em>z</em>-test for the hypothesis testing.

The test statistic is:

z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3

Thus, the test statistic value is 15.3.

7 0
2 years ago
A school district has a student population of $6,734 students. If the maximum class size is 25 students. How many more teacher m
emmasim [6.3K]

Answer:

53 teachers

Step-by-step explanation:

Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:

6,734 / 25 = 269.36

Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).

If we take 269 teachers and 25 students per class, we get:

269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.

That means that the number of teachers needed is 270.

It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.

8 0
2 years ago
Selma’s class is making care packages to give to victims of a natural disaster. Selma packs one box in 5 minutes and has already
luda_lava [24]
I'm not sure what your asking, but if your asking how long it took her, it took her one hour. There is 12 boxes, and each one took her 5 minutes. 12*5 is equal to 60.
6 0
2 years ago
A random survey was taken in Centerville. People in twenty-five homes were asked how many cars were registered to their househol
Ulleksa [173]
In order to find the mean, you first count how many numbers are there. Then, you add all numbers together and divide them by the total of numbers. In this case, you would add (1+2+1+0+3+4+0+1+1+1+2+2+3+2+3+2+1+4+0+0+2+2+1+1+1), which equals to 40. The total of numbers is 25. You divide 40 by 25, and it would get you 1.6. Therefore, your mean is 1.6.

To calculate the median, you list the numbers from least to greatest, and find the middle number. The list for this survey would be 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4. The middle number of this list is 1, therefore, your median is 1.

The mode is simply the number that appears the most in this list. There are 4 zeroes, 9 ones, 7 twos, 3 threes, and 2 fours. The most in this list would be 1, because there are 9 of them. Your mode is 1.

Mean - 1.6
Median - 1
Mode - 1

Answer: A. 1.6, 1, 1


8 0
2 years ago
Read 2 more answers
Radium decays according to the function Q(t) = Q0e-kt where Q represents the quantity remaining after t years and k is the decay
Bingel [31]
Solve

hmmm
half life
well, 120 to 60 is half

60=120e^(-0.00043t)
solve for t
divide both sides by 120
1/2=e^(-0.00043t)
take ln of both sides
ln(1/2)=-0.00043t
divide both sides by -0.00043
ln(1/2)/-0.00043=t
t≈1611.97 years
about 1612 years
3 0
2 years ago
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