1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Darina [25.2K]
3 years ago
11

A dart is to be thrown at a target. The probability the dart will hit the target (yes or no) on a single attempt is 0.20. Each t

hrow is independent of the other throws. Let X be the number of attempts before the target is hit.
a. What type of distribution does X follow?
b. Compute the expected number of attempts needed before hitting the target?
c. What is the variance and standard deviation of the number of attempts needed before hitting the target?
d. What is the probability that it will take less than 5 throws before hitting the target?
Mathematics
1 answer:
natima [27]3 years ago
7 0

Answer:

a) X has geometric distribution with parameter 0.2

b) The expected number of attempts before hitting the target is 5

c) The variance is 20, the standard deviation is √20

d) The probability that less than 5 throws are needed before hitting the target is 0.5904.

Step-by-step explanation:

a) X has geometric distribution, with parameter p=0.2.

b) If X is geometric with parameter p, then its mean is 1/p and the variance is \frac{1-p}{p^2} . With p = 0.2, the mean is 1/0.2 = 5. As a consecuence, the expected number of attempts before hitting the target is 5.

c) The variance with p = 0.2 is 0.8/0.2² = 20. The standard deviation is √20.

d) The probability that it takes less than 5 throws before hitting the target can be computed with the probability of the complementary event: the probability that the first 4 targets miss. That probability is 0.8⁴=0.4096. Therefore, the probability that it will take less than 5 throws before hitting the target is 1-0.4096 = 0.5904.

You might be interested in
How do i check an equation for extraneous solutions?
Marina86 [1]
Example:

\sqrt x(x+1)=0

This suggests two solutions, x=0 and x=-1.

However, upon plugging these solutions back into the equation, you get

\sqrt0(0+1)=0(1)=0

which checks out, but

\sqrt{-1}(1-1)=0

does not because \sqrt x is defined only for x\ge0 (assuming you're looking for real solutions only). So, we call x=-1 an extraneous solution, and the complete solution set (over the real numbers) is x=0.
7 0
3 years ago
Read 2 more answers
Does the chart below represent a proportional relationship? What is the rate of change?
Lilit [14]

This chart represents a proportional relationship. The rate of change will be 4.

<h3>What is the constant of proportionality?</h3>

Firstly, there is a proportional relationship.

Two values x  and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called the constant of proportionality.

Given;

x y

1 4

2 8

3 12

4 16

Here, x = ky

put the first value

k = 1/4

This chart represents a proportional relationship.

So the rate of change will be

Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\Rate = \dfrac{8 - 4}{2 - 1}\\\\Rate = 4

Learn more about proportional ;

brainly.com/question/20048815

#SPJ1

5 0
2 years ago
The area of a rectangle is 45 sq ft. its perimeter is 36 ft. Find the length and width.
mr_godi [17]
You have to divide 36 and 2
8 0
3 years ago
Read 2 more answers
Simplify 5 √16 + 12 √54 - 3 √8
USPshnik [31]

20+36. l6-6/2

v. v

decimal form

99.69634936

8 0
2 years ago
32 53 24 54 61 13<br>17 36 04 10 51 68​
Leno4ka [110]

Answer:

<u>32 53 24 54 61 13</u>

<u>32 53 24 54 61 1317 36 04 10 51 68</u>

7 0
3 years ago
Other questions:
  • Gillian bought some bund and cakes for $15.25. A bun and a cake cost $2 altogether and each cake cost $1.25. She bought one more
    7·1 answer
  • If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, what is the height of the cup?
    14·1 answer
  • Suppose a scientis cools 3 gases will the temperature be negative or positive
    5·1 answer
  • In a survey of U.S. adults with a sample size of 2062​,330said Franklin Roosevelt was the best president since World War II. Two
    5·1 answer
  • F(x) = x2 + 3 <br><br> Is it an even odd function, both or neither?
    8·2 answers
  • There are 9 acts in a talent show.
    8·2 answers
  • What inverse operations do you use to solve for b?<br><br> -9 = -11 + b/8
    15·1 answer
  • What is the length of the longer side ?
    10·1 answer
  • 3.
    14·2 answers
  • Series of math questions
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!