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yan [13]
3 years ago
12

A coin is tossed 100 times. Consider the following statements:

Mathematics
1 answer:
shusha [124]3 years ago
4 0

Answer:

1. and III.

Step-by-step explanation:

Option 1 and 3 are correct.

The probability of landing on heads would be 1/2, so 50 times in 100. This is the expected outcome, so option 1 is correct.

However, that is just the most probable outcome, probability is almost never 100% accurate. Therefore, the number of heads will most likely be 50, give or take 5 or so. Therefore, option 3 is also correct.

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11. Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x) 5 5 0 x , 0
NISA [10]

Question not properly presented

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x)

0 ------ x<0

x²/25 ---- 0 ≤ x ≤ 5

1 ----- 5 ≤ x

Use the cdf to obtain the following.

(a) Calculate P(X ≤ 4).

(b) Calculate P(3.5 ≤ X ≤ 4).

(c) Calculate P(X > 4.5)

(d) What is the median checkout duration, μ?

e. Obtain the density function f (x).

f. Calculate E(X).

Answer:

a. P(X ≤ 4) = 16/25

b. P(3.5 ≤ X ≤ 4) = 3.75/25

c. P(4.5 ≤ X ≤ 5) = 4.75/25

d. μ = 3.5

e. f(x) = 2x/25 for 0≤x≤2/5

f. E(x) = 16/9375

Step-by-step explanation:

a. Calculate P(X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(X ≤ 4) = F(x) {0,4}

P(X ≤ 4) = x²/25 {0,4}

P(X ≤ 4) = 4²/25

P(X ≤ 4) = 16/25

b. Calculate P(3.5 ≤ X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(3.5 ≤ X ≤ 4) = F(x) {3.5,4}

P(3.5 ≤ X ≤ 4) = x²/25 {3.5,4}

P(3.5 ≤ X ≤ 4) = 4²/25 - 3.5²/25

P(3.5 ≤ X ≤ 4) = 16/25 - 12.25/25

P(3.5 ≤ X ≤ 4) = 3.75/25

(c) Calculate P(X > 4.5).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(4.5 ≤ X ≤ 5) = F(x) {4.5,5}

P(4.5 ≤ X ≤ 5) = x²/25 {4.5,5}

P(4.5 ≤ X ≤ 5)) = 5²/25 - 4.5²/25

P(4.5 ≤ X ≤ 5) = 25/25 - 20.25/25

P(4.5 ≤ X ≤ 5) = 4.75/25

(d) What is the median checkout duration, μ?

Median is calculated as follows;

∫f(x) dx {-∝,μ} = ½

This implies

F(x) {-∝,μ} = ½

where F(x) = x²/25 for 0 ≤ x ≤ 5

F(x) {-∝,μ} = ½ becomes

x²/25 {0,μ} = ½

μ² = ½ * 25

μ² = 12.5

μ = √12.5

μ = 3.5

e. Calculating density function f (x).

If F(x) = ∫f(x) dx

Then f(x) = d/dx (F(x))

where F(x) = x²/25 for 0 ≤ x ≤ 5

f(x) = d/dx(x²/25)

f(x) = 2x/25

When

F(x) = 0, f(x) = 2(0)/25 = 0

When

F(x) = 5, f(x) = 2(5)/25 = 2/5

f(x) = 2x/25 for 0≤x≤2/5

f. Calculating E(X).

E(x) = ∫xf(x) dx, 0,2/5

E(x) = ∫x * 2x/25 dx, 0,2/5

E(x) = 2∫x ²/25 dx, 0,2/5

E(x) = 2x³/75 , 0,2/5

E(x) = 2(2/5)³/75

E(x) = 16/9375

4 0
2 years ago
On the graph of the equation 5x - y = 8, the point whose y-coordinate is 7 has an x-coordinates of ?
Lemur [1.5K]

Answer:

x = 3

Step-by-step explanation:

To find the x-coordinate, substitute y = 8 into the equation abd solve for x

5x - 7 = 8 ( add 7 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3

Thus (3, 7) is a solution to the equation


3 0
3 years ago
Read 2 more answers
What is the solution set of the equation X/5 + x/2 =14?
JulijaS [17]

Answer:

x= 20

Step-by-step explanation:

Solve for x:

(7 x)/10 = 14

Multiply both sides of (7 x)/10 = 14 by 10/7:

(10×7 x)/(7×10) = 10/7×14

10/7×7/10 = (10×7)/(7×10):

(10×7)/(7×10) x = 10/7×14

10/7×14 = (10×14)/7:

(10×7 x)/(7×10) = (10×14)/7

(10×7 x)/(7×10) = (7×10)/(7×10)×x = x:

x = (10×14)/7

14/7 = (7×2)/7 = 2:

x = 10×2

10×2 = 20:

Answer:  x = 20

7 0
3 years ago
You are planning a party. You want to rent a snow cone machine, and the snow cone company charges a $25 set-up fee plus $15 per
dezoksy [38]
The answer would be 15h+25 because h isthe variable representing hours and they charge $15 for every hour. And also, the plus 25 is for the setup fee.
5 0
3 years ago
Read 2 more answers
Principle: $6500 Rate: 3%
Nikitich [7]

Answer:

Step-by-step explanation:

A)Initial amount deposited into the account is $6500 This means that the principal is P, so

P = 500

It was compounded daily. This means that it was compounded 360 times in a year. So

n = 360

The rate at which the principal was compounded is 3%. So

r = 3/100 = 0.03

It was compounded for 5 years. So

t = 5

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 6500 (1+0.03/360)^360×5

A = 6500 (1+0.00008333333)^360×5

A = 6500 (1.00008333333)^1800

A = $7551.70

B) The interest earned is Total amount earned - principal. It becomes

7551.7 - 6500 = $1051.7

6 0
3 years ago
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