the probability distribution below represents the number of toppings per pizza sold at certain pizza restaurant.
|x|p(x)|
|0|0.29|
|1|0.36|
|2|0.11|
|3|0.07|
|4|0.17|
round answers to 2 decimals when appropriate.
find the mean number of toppings sold per pizza.
μ =
find the standard deviation of the number of pizza toppings sold per pizza.
σ =

Question

Accepted Answer

# Explanation:
## Step1: Recall mean formula
The mean $\mu$ of a discrete - probability distribution is given by $\mu=\sum_{i}x_{i}P(x_{i})$.
$$
\begin{align*}
\mu&=(0\times0.29)+(1\times0.36)+(2\times0.11)+(3\times0.07)+(4\times0.17)\
&=0 + 0.36+0.22 + 0.21+0.68\
&=1.47
\end{align*}
$$
## Step2: Recall variance formula
The variance $\sigma^{2}=\sum_{i}(x_{i}-\mu)^{2}P(x_{i})$.
$$
\begin{align*}
&(0 - 1.47)^{2}\times0.29+(1 - 1.47)^{2}\times0.36+(2 - 1.47)^{2}\times0.11+(3 - 1.47)^{2}\times0.07+(4 - 1.47)^{2}\times0.17\
&=( - 1.47)^{2}\times0.29+( - 0.47)^{2}\times0.36+(0.53)^{2}\times0.11+(1.53)^{2}\times0.07+(2.53)^{2}\times0.17\
&=2.1609\times0.29 + 0.2209\times0.36+0.2809\times0.11+2.3409\times0.07+6.4009\times0.17\
&=0.626661+0.079524 + 0.030899+0.163863+1.088153\
&=1.9891
\end{align*}
$$
## Step3: Calculate standard - deviation
The standard deviation $\sigma=\sqrt{\sigma^{2}}$. So $\sigma=\sqrt{1.9891}\approx1.41$.

# Answer:
$\mu = 1.47$
$\sigma\approx1.41$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall mean formula

Step2: Recall variance formula

Step3: Calculate standard - deviation

Answer:

x	p(x)
0	0.29
1	0.36
2	0.11
3	0.07
4	0.17