Mathematics, 06.05.2020 03:04 tbiles99

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.7 and standard deviation 0.75. (a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.7 and 3.00?b) How large a sample size would be required to ensure thatthe first probability in part (a) is at least .99 ??

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Answer from: valenzueladomipay09u

(a) The probability that the sample average sediment density is at most 3.00 is 0.092.

The probability that the sample average sediment density is between 2.70 and 3.00 is 0.477.

(b) The sample size must be at least 77.

Step-by-step explanation:

The random variable X ca be defined as the sediment density (g/cm) of a specimen from a certain region.

The random variable X is normally distributed with mean, μ = 2.7 and standard deviation, σ = 0.75.

(a)

A random sample of n = 25 specimens is selected.

Compute the probability that the sample average sediment density is at most 3.00 as follows:

Apply continuity correction:

$P(\bar X\leq 3.00)=P(\bar X$

$=P(\bar X$

$=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}$

=P(Z

Thus, the probability that the sample average sediment density is at most 3.00 is 0.092.

Compute the probability that the sample average sediment density is between 2.70 and 3.00 as follows:

P(2.70

=P(0

*Use a z-table.

Thus, the probability that the sample average sediment density is between 2.70 and 3.00 is 0.477.

(b)

It is provided that:

$P(\bar X\leq 3.00)\geq 0.99$

$P(\bar X$

$P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}$

P(Z

The value of z for the probability above is

z ≥ 2.33

Compute the value of n as follows:

$\frac{|2.50-2.70|}{0.75/\sqrt{n}}\geq 2.33$

$\frac{|-0.20|}{2.33}\geq \frac{0.75}{\sqrt{n}}$

$\sqrt{n}\geq \frac{0.75\times 2.33}{|-0.20|}\\\sqrt{n}\geq 8.7375\\n\geq 76.3439\\\approx n\geq 77$

Thus, the sample size must be at least 77.

Answer from: Quest

What are the following algebraic equations. you need to post those if you want the answer

Answer from: Quest

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2 is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes. our only condition is that it passes through the point (-2,5)

A. write an equation of a line that passes through (-2, 5). b. how many different equations could y

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Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normall...