8.12 Variability of samples from distributions
Interactive practice questions
Consider a fair $8$8 sided die with faces labeled from $1$1 to $8$8.
Let $X$X be the outcome when the die is rolled.
Complete the table of values for the probability distribution for $X$X.
| $x$x | $1$1 | $2$2 | $3$3 | $4$4 | $5$5 | $6$6 | $7$7 | $8$8 |
|---|---|---|---|---|---|---|---|---|
| $P\left(X=x\right)$P(X=x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Calculate the mean of the distribution.
Calculate the standard deviation of the distribution correct to two decimal places.
The die was rolled 20 times with the following results
| $8$8 | $4$4 | $1$1 | $7$7 | $5$5 |
| $2$2 | $4$4 | $8$8 | $2$2 | $6$6 |
| $3$3 | $6$6 | $3$3 | $5$5 | $3$3 |
| $1$1 | $5$5 | $5$5 | $5$5 | $8$8 |
Calculate the sample mean of the results.
Calculate the sample standard deviation.
Round your answer to two decimal places.
The random variable $X$X is uniformly distributed with a variance of $\frac{25}{12}$2512 over the interval $1\le x\le6$1≤x≤6.
$R$R is a binomial variable with $n=14$n=14 and $p=0.25$p=0.25.
Two samples, $A$A and $B$B, each of size $10$10, are taken from $R$R and tabulated below.
The normal variable $X$X has a mean of $120$120 and a standard deviation of $15$15.
Two samples, $A$A and $B$B, each of size $10$10, are taken from $X$X and tabulated below.