Find the distance between each pair of points.

The proportion of high school seniors who are married is 0.02. Suppose we take a random sample of 300 high school seniors; a.) F

cricket20 [7]

Answer:

a) Mean 6, standard deviation 2.42

b) 10.40% probability that, in our sample of 300, we find that 8 of the seniors are married.

c) 14.85% probability that we find less than 4 of the seniors are married.

d) 99.77% probability that we find at least 1 of the seniors are married

Step-by-step explanation:

For each high school senior, there are only two possible outcomes. Either they are married, or they are not. The probability of a high school senior being married is independent from other high school seniors. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that:

$n = 300, p = 0.02$

a.) Find the mean and standard deviation of the sample count X who are married.

Mean

$E(X) = np = 300*0.02 = 6$

Standard deviation

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.02*0.98} = 2.42$

b.) What is the probability that, in our sample of 300, we find that 8 of the seniors are married?

This is P(X = 8).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{300,8}.(0.02)^{8}.(0.98)^{292} = 0.1040$

10.40% probability that, in our sample of 300, we find that 8 of the seniors are married.

c.) What is the probability that we find less than 4 of the seniors are married?

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{300,0}.(0.02)^{0}.(0.98)^{300} = 0.0023$

$P(X = 1) = C_{300,1}.(0.02)^{1}.(0.98)^{299} = 0.0143$

$P(X = 2) = C_{300,2}.(0.02)^{2}.(0.98)^{298} = 0.0436$

$P(X = 3) = C_{300,3}.(0.02)^{3}.(0.98)^{297} = 0.0883$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0023 + 0.0143 + 0.0436 + 0.0883 = 0.1485$

14.85% probability that we find less than 4 of the seniors are married.

d.) What is the probability that we find at least 1 of the seniors are married?

Either no seniors are married, or at least 1 one is. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

From c), we have that $P(X = 0) = 0.0023$ . So

$0.0023 + P(X \geq 1) = 1$

$P(X \geq 1) = 0.9977$

99.77% probability that we find at least 1 of the seniors are married

3 0

3 years ago

Craig collects coins. He collected a total of 225 coins. If 88% of coins he collected were foreign, how many other coins did he

agasfer [191]

Answer:

27

Step-by-step explanation:

In this case we associate in total value from 225 to 100%, and they tell us that foreign currencies represent 88%, therefore, in quantity this would be:

225 * 88/100

198

The rest of the coins would then refer to the other coins I collect, which would be:

225 - 198 = 27

That is, 27 coins are the remaining coins.

5 0

3 years ago

3 Which of the Great Lakes, if any, is entirely above sea level? Explain.

Firdavs [7]

Answer:

Lake Michigan and Lake Huron

Step-by-step explanation:

Lake Michigan and Lake Huron - two of North America's Great Lakes - are contiguous and they share the same elevation of 577 feet above sea level. They are connected by the five-mile-wide Straits of Mackinac. Hydrologically, this makes these "two lakes" a single lake.

Some hydrologists designate the combined entity of Lake Michigan and Lake Huron as "Lake Michigan-Huron."

4 0

4 years ago

Minimize the objective function P = 45x + 48y for the given constraints.

BabaBlast [244]

Answer:

Following are the solution to the given equation:

Step-by-step explanation:

The graph file and correct question are defined in the attachment please find it.

According to the linear programming principle, we predict, that towards the intersections of the constraint points in the viability area, and its optimal solution exists. The sketch shows the points that are (0,16), (3,1), and (6,0).

by putting each point value into the objective function:

$\to P(0,16) = 768\\\\\to P(3,1) = 183\\\\\to P(6,0) = 270$

Thus, the objective of the function is reduced with a value of 183 at (3,1).

5 0

3 years ago

Is the area of the shaded rectangle 6(2−m) or 6(m−2)?<br>Explain how you know.

Rzqust [24]

Answer:

6(2-m)

Step-by-step explanation:

the m could not be times only two so the answer would have been 12-m no matter what you don't add or subtract or times the letter because unless if the number had the same letter!

Hope this helps!! if it doesnt i apalogize!! god bless!! - Natalia

6 0

3 years ago

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