3. rish florist determines the probabilities for the number of flower arrangements they deliver each day.
x 6 7 8 9 10
p(x) 0.2 0.2 0.3 0.2 0.1
a. find the mean, variance, and standard deviation.
e(x) μ=
σ²=
σ=
b. approximately how many arrangements should rish expect to deliver each week?

Question

Accepted Answer

# Explanation:
## Step1: Calculate the mean ($\mu$)
The formula for the mean of a discrete random variable is $\mu=\sum_{i}x_{i}P(x_{i})$.
$$
\begin{align*}
\mu&=(6\times0.2)+(7\times0.2)+(8\times0.3)+(9\times0.2)+(10\times0.1)\
&=1.2 + 1.4+2.4 + 1.8+1\
&=7.8
\end{align*}
$$
## Step2: Calculate the variance ($\sigma^{2}$)
The formula for the variance is $\sigma^{2}=\sum_{i}(x_{i}-\mu)^{2}P(x_{i})$.
$$
\begin{align*}
(6 - 7.8)^{2}\times0.2&=(-1.8)^{2}\times0.2=3.24\times0.2 = 0.648\
(7 - 7.8)^{2}\times0.2&=(-0.8)^{2}\times0.2=0.64\times0.2=0.128\
(8 - 7.8)^{2}\times0.3&=(0.2)^{2}\times0.3=0.04\times0.3 = 0.012\
(9 - 7.8)^{2}\times0.2&=(1.2)^{2}\times0.2=1.44\times0.2=0.288\
(10 - 7.8)^{2}\times0.1&=(2.2)^{2}\times0.1=4.84\times0.1 = 0.484\
\sigma^{2}&=0.648+0.128 + 0.012+0.288+0.484\
&=1.56
\end{align*}
$$
## Step3: Calculate the standard deviation ($\sigma$)
The standard deviation is the square - root of the variance, $\sigma=\sqrt{\sigma^{2}}$.
$$
\sigma=\sqrt{1.56}\approx1.25
$$
## Step4: Calculate the expected number of arrangements per week (part b)
Assuming a week has 7 days. The expected number of arrangements per day is $\mu = 7.8$. So the expected number per week is $7\times\mu$.
$$
7\times7.8 = 54.6\approx55
$$

# Answer:
a. Mean ($\mu$) = $7.8$, Variance ($\sigma^{2}$) = $1.56$, Standard deviation ($\sigma$) $\approx1.25$; b. Approximately $55$ arrangements.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the mean ($\mu$)

Step2: Calculate the variance ($\sigma^{2}$)

Step3: Calculate the standard deviation ($\sigma$)

Step4: Calculate the expected number of arrangements per week (part b)

Answer: