Question

A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed

Answer 1

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

Answer 2

The standard deviation for the number of heads that will be tossed is $\boxed{4.24}.$

Further Explanation:

The random variable X follows binomial distribution.

$\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}$

Here, n represents the total number of experiments and p denotes the probability of the event.

Apply central limit theorem.

$\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}$

The mean of the binomial distribution can be calculated as follows,

$\boxed{{\text{Mean}} = n \times p}$

The standard deviation of binomial distribution can be calculated as follows,

$\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }$

Given:

Coin is tossed 72 times.

Explanation:

Consider X is the random variable that head will occur.

The probability of head occur is $p = \dfrac{1}{2}.$

The mean can be calculated as follows,

$\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}$

The standard deviation of the number of heads can be calculated as follows,

$\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}$

Hence, the standard deviation for the number of heads that will be tossed is $\boxed{4.24}.$

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.