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
Slav-nsk [51]
3 years ago
8

When we toss a coin, there are two possible outcomes: a head or a tail. Suppose that we toss a coin 100 times. Estimate the appr

oximate probability that the number of tails is between 40 and 60. Explain your reasoning step by step
Mathematics
1 answer:
marin [14]3 years ago
8 0

Answer:

96.42% probability that the number of tails is between 40 and 60.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

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)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

100 tosses, so n = 100

Two outcomes, both equally as likely. So p = \frac{1}{2} = 0.5

So

E(X) = np = 100*0.5 = 50

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5

Estimate the approximate probability that the number of tails is between 40 and 60.

Using continuity correction.

P(40 - 0.5 \leq X \leq 60 + 0.5) = P(39.5 \leq X \leq 60.5)

This is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 39.5. So

X = 60.5

Z = \frac{X - \mu}{\sigma}

Z = \frac{60.5 - 50}{5}

Z = 2.1

Z = 2.1 has a pvalue of 0.9821

X = 39.5

Z = \frac{X - \mu}{\sigma}

Z = \frac{39.5 - 50}{5}

Z = -2.1

Z = -2.1 has a pvalue of 0.0179

0.9821 - 0.0179 = 0.9642

96.42% probability that the number of tails is between 40 and 60.

You might be interested in
Which mixed number is equivalent to the improper fraction?
o-na [289]

Answer:

B: 2 7/8

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Need help somebody pleaseee
horsena [70]

Answer:

The second one I believe

8 0
3 years ago
{(1,3), (2, 5), (3,-4), (4, -3), (5, -1)} The above is DONE<br><br>Function or not a Function?​
Hoochie [10]

Answer:

Yes it is a Function

Step-by-step explanation:

Because there are no same x-values with the same y-values

3 0
3 years ago
A planet has a circular orbit around a star. It is a distance of 81,000,000 km from the centre of the star. It orbits at an aver
slava [35]

81,000,000 \text{ km} \left(\frac{1 \text{ h}}{46,000 \text{ km}} \right) =\frac{40500}{23} \text{ h} \\ \\ \frac{40500}{23} \text{ h} \left(\frac{1 \text{ days}}{24 \text{ hours}} \right) \approx \boxed{73 \text{ days}}

5 0
2 years ago
What is this answer?
zhannawk [14.2K]

I'm NOT 100% confident in my answers.

Graph 1:

Range: Option B

Graph 2:

Range: Option A

The range has to start at zero since that's the lowest point we can go, only one with zero is first option.

RATE AS BRAINLIEST

8 0
2 years ago
Other questions:
  • Whats 34+54+72=? ............................................
    8·1 answer
  • There are 12 different pizza toppings, and Arturo must rank his top 4 in order. How many different possible rankings are there?
    5·1 answer
  • The first term in the sequence is 1, and each other term is 5 more than three times the previous term.
    15·1 answer
  • What is 45+(-15) +7
    15·1 answer
  • What is the value of x? Show your work each step of the way. No work means NO points!
    11·1 answer
  • A gumball machine contains 23 green gumballs, 52 red gumballs, 34 blue gumballs, 61 yellow gumballs, and 300 pink gumballs. What
    10·2 answers
  • What the answer fast now
    13·2 answers
  • A sailboat's Saul has three sides that are all the same length. Each side measures x - 10 units. The sail's perimeter is 63 unit
    13·1 answer
  • Please help jkjk but thanks you no need to answer free
    12·2 answers
  • HELP WITH MY GEOMETRY REVIEW
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!