Answer :
Answer:
(b)$29.62
(c)$5.73
Step-by-step explanation:
Basic: Standard internet for everyday needs, at $24.95 per month.
Premium: Fast internet speeds for streaming video and downloading music, at $30.95 per month.
Ultra: Super-fast internet speeds for online gaming at $40.95 per month.
Let the number of customers on Ultra=x; therefore:
Number of Premium customers =2x
Number of Basic customers =3x
Total=x+2x+3x=6x
[tex]P(Ultra)=\dfrac{x}{6x}=\dfrac{1}{6} \\P(Premium)=\dfrac{2x}{6x}=\dfrac{1}{3}\\P(Basic)=\dfrac{3x}{6x}=\dfrac{1}{2}[/tex]
(a)X=Monthly fee paid by a randomly selected customer.
Therefore, the probability distribution of X is given as:
[tex]\left|\begin{array}{c|c}X&P(X)\\---&---\\\$24.95&3/6\\\$30.95&2/6\\\$40.95&1/6\end{array}\right|[/tex]
(b)Average Monthly Revenue per customer
Mean,
[tex]\mu=(\$24.95 \times 3/6)+(\$30.95 \times 2/6)+(\$40.95 \times 1/6)\\=\$29.62[/tex]
(c)Standard Deviation
[tex]\left|\begin{array}{c|c|c|c|c}x&P(x)&x-\mu &(x-\mu)^2&(x-\mu)^2P(x)\\-----&-----&----&----&-----\\\$24.95&3/6&-4.67&21.8089&10.9045\\\$30.95&2/6&1.33&1.7689&0.5896\\\$40.95&1/6&11.33&128.3689&21.3948\\-----&-----&----&----&-----\\&&&&32.8889\end{array}\right|[/tex]
[tex]\text{Standard Deviation}=\sqrt{(x-\mu)^2P(x)}\\=\sqrt{32.8889} \\ \sigma=\$5.73[/tex]