The median of the data set is 18 what number is missing 12,17,21,13,25

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

Use deductive reasoning to prove that x = 10 is the solution equation 3x – 7 = 23. Be sure to

Sphinxa [80]

Answer:

Step-by-step explanation:

3x-7=23

<=> 3x = 23 + 7

<=> 3x = 30

<=> X = 30 ÷ 3

<=> X = 10

5 0

3 years ago

6. Find the total bill:

daser333 [38]

First multiply all the items up with their correct prices.

5 Golf Clubs = 18.65 each

5 x 18.65 = 93.25

60 Golf Balls = 16.50 per dozen

60 = 5 dozen

5 x 16.50 = 82.5

1 pair of golf shoes = 75.80

1 x 75.80 = 75.80

Now, add them all up.

93.25 + 82.5 + 75.80 = 251.55

Lastly, multiply by 1.15 to add the 15% sales tax.

251.55 x 1.15 = 289.28

Thus, the total cost of all the equipment with tax is $289.28

7 0

3 years ago

URGENT NEED HELP ON THIS

zvonat [6]

Answer:

I think option no B

hope it will help you

5 0

2 years ago

Read 2 more answers

Check whether the points ( -2, 3) , (8,3) ,(6,7) are the vertices of a right triangle

lora16 [44]

Answer:

Given coordinetes of triangle A(−2,3),B(8,3) and C(6,7)

AB=

[8−(−2)]

2

+(3−3)

2

=

(10)

2

+(0)

2

=

100

AC=

[6−(−2)]

2

+(7−3)

2

=

(8)

2

+(4)

2

=

64+16

=

80

BC=

(6−8)+[7−(2)]

2

=

(−2)

2

+(4)

2

=

4+16

=

20

If ABC is a right angled triangle, then square of one side must be equal to sum of suare of other two sides.

AB

2

=(

100

)

2

=100

and AC

2

+BC

2

=(

80

)

2

+(

20

)

2

=100

∴AB

2

=AC

2

+BC

2

thus triangle satisfies the Pythagoras theorem

Hence, the triangle is right angled triangle.

Step-by-step explanation:

8 0

3 years ago