Question

A standard die is rolled 360 times in hopes of rolling a 5 or 6 to the probability of success is p=1/3 find the standard deviation of the binomial distribution

Answer 1

Answer:

The standard deviation is $8.94$ to the nearest hundredth.

Step-by-step explanation:

The standard deviation of a binomial distribution is calculated using the formula;

$\sigma =\sqrt{npq}$, where

$n=360$ is the number of times the die is rolled.

$p=\frac{1}{3}$ is the probability of a success and $q=1-\frac{1}{3} =\frac{2}{3}$ is the probability of a failure, that is not rolling a 5 or 6.

We substitute all these values in to the formula, to obtain,

$\sigma =\sqrt{360\times \frac{1}{3} \times \frac{2}{3}}$

$\Rightarrow \sigma =\sqrt{80}$

$\Rightarrow \sigma =4\sqrt{5}$

$\Rightarrow \sigma =8.94$ to the nearest hundredth.

Answer 2

Answer: 1. B) 53.4

2. C) 128.7

3. A) usual because the result is between...

4. A) 0.9

5. A) 8.9

6. D) 92.8

7. C) 131.7

8. A) 372.6

9. D) 43.7

10. D) 240.8

Step-by-step explanation: 100% :)