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
andrezito [222]
2 years ago
12

An honest die is rolled. If the roll comes out even (2, 4, or 6), you will win $1; if the roll comes out odd (1,3, or 5), you wi

ll lose $1, Suppose that in one evening you play this game n=2500 times in a row.
(a) Estimate the probability that by the end of the evening you will not have lost any money.
(b) Estimate the probability that the number of "even rolls" (roll a 2, 4, or 6) will fall between 1250 and 1300.
(c) Estimate the probability that you will win $100 or more.
Mathematics
1 answer:
jenyasd209 [6]2 years ago
7 0

Answer:

(a) 50%

(b) 47.5%

(c) 2.5%

Step-by-step explanation:

According to the honest coin principle, if the random variable <em>X</em> denotes the number of heads in <em>n</em> tosses of an honest coin (<em>n</em> ≥ 30), then <em>X</em> has an approximately normal distribution with mean, \mu=\frac{n}{2} and standard deviation, \sigma=\frac{\sqrt{n}}{2}.

Here the number of tosses is, <em>n</em> = 2500.

Since <em>n</em> is too large, i.e. <em>n</em> = 2500 > 30, the random variable <em>X</em> follows a normal distribution.

The mean and standard deviation are:

\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25

(a)

To not lose any money the even rolls has to be 1250 or more.

Since, <em>μ</em> = 1250 it implies that the 50th percentile is also 1250.

Thus, the probability that by the end of the evening you will not have lost any money is 50%.

(b)

If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.

Then for number of "even rolls" as 1300,

1300 = 1250 + 2 × 25

        = μ + 2σ

Then P (μ + 2σ) for a normally distributed data is 0.975.

⇒ 1300 is at the 97.5th percentile.

Then the area between 1250 and 1300 is:

Area = 97.5% - 50%

        = 47.5%

Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.

(c)

To win $100 or more the number of even rolls has to at least 1300.

From part (b) we now 1300 is the 97.5th percentile.

Then the probability that you will win $100 or more is:

P (Win $100 or more) = 100% - 97.5%

                                   = 2.5%.

Thus, the probability that you will win $100 or more is 2.5%.

You might be interested in
What is the apparent solution to the system of equations graphed above?
Oksana_A [137]
I think the answer is (-2,2)
7 0
3 years ago
Read 2 more answers
Assume that
JulsSmile [24]

Answer:

D - It is impossible to make a judgment with the given information.

Step-by-step explanation:

The fact that 1200 births were randomly selected and only 599 of such picks are girls does not give enough information on whether the birth is significantly high, low or neither. We must have other information to test for significance of the births proportion.

All we know is that;

Proportion of girls birth (p) = 599/1200 = 0.499. And by default, the proportion of male births (q) will be 1-p = 1-0.499 = 0.501.

If we examine the proportion closely, there seems to be no significant difference in the birth proportion.

Having said this, we cannot really imply that, the number of girls is significantly high. Or the number of girls is neither significantly low nor significantly high. Or the number of girls is significantly low.

The best subjective submission will be that, <em>there is no significant difference between girls birth and males birth.</em> The question of high or low (an alternative hypothesis) requires some further statistical test and this question does not provide further details.

8 0
3 years ago
10PTS PLEASE HELP!!!!!!!
Nostrana [21]

The equation of a circle:

(x-h)^2+(y-k)^2=r^2

(h, k) - a coordinates of the center

r - a radius

A diameter d = 2r

We have

x^2+(y-2)^2=100\to r^2=100\to r=\sqrt{100}\to r=10

Answer: d = 2 · 10 = 20

6 0
3 years ago
A hiker walks at a speed of 3 2 5 kilometers per hour. How many kilometers will the hiker walk-in
Leto [7]

Answer:

65 km

Step-by-step explanation:

was that 325 km? if so it would be 325 x 5 = 65

3 0
2 years ago
Read 2 more answers
Which correctly represents the probability 1 as a percent?
In-s [12.5K]

Answer:

0.01

Step-by-step explanation:

if you meant a to be .01 than it's that good luck

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the mode for the data set?
    8·2 answers
  • How do i turn a decimal into a fraction
    12·2 answers
  • 45 + 5 = what i need so HELP
    6·2 answers
  • What percentage give4/7​
    15·1 answer
  • Need help I’m stuck on this one. I should ask my teacher but I get help from here faster. Need the answer ASAP. Thank you guys s
    10·1 answer
  • 8/6+9/3=<br> Find the value of this
    12·2 answers
  • Mr Lorenzo must make a minimum of 48 circuit boards per day. On Wednesday he made 60. What percent of required minimum did he ma
    9·1 answer
  • Evaluate when <br> a =3 b= 4.5 and h = 6
    11·1 answer
  • Help me please (I need write more something in order to I can submit answer)​
    5·2 answers
  • 15. Find the following bases.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!