Respuesta :
The probability of obtaining a head or tail in tossing a coin is modeled by the binomial distribution.
The probability of obtaining heads (success) is p = 1/2.
In n tosses, the expected statistical parameters are
m = np, the mean
σ = √[np(1-p)]
In 72 tosses of the coin, the standard deviation for the number of heads obtained is
σ = √[72*(0.5)*(0.5)]
= 4.243
Answer: 4.243
The probability of obtaining heads (success) is p = 1/2.
In n tosses, the expected statistical parameters are
m = np, the mean
σ = √[np(1-p)]
In 72 tosses of the coin, the standard deviation for the number of heads obtained is
σ = √[72*(0.5)*(0.5)]
= 4.243
Answer: 4.243
The standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
Further Explanation:
The random variable X follows binomial distribution.
[tex]\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}[/tex]
Here, n represents the total number of experiments and p denotes the probability of the event.
Apply central limit theorem.
[tex]\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}[/tex]
The mean of the binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Mean}} = n \times p}[/tex]
The standard deviation of binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }[/tex]
Given:
Coin is tossed 72 times.
Explanation:
Consider X is the random variable that head will occur.
The probability of head occur is [tex]p = \dfrac{1}{2}.[/tex]
The mean can be calculated as follows,
[tex]\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}[/tex]
The standard deviation of the number of heads can be calculated as follows,
[tex]\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}[/tex]
Hence, the standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589
Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial Distribution
Keywords: coin, tossed 72 times, number of heads, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.
