Question

Internet Pricing An Internet Service Provider (ISP) offers its customers three options:

Answer 1

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

$P(Ultra)=\dfrac{x}{6x}=\dfrac{1}{6} \\P(Premium)=\dfrac{2x}{6x}=\dfrac{1}{3}\\P(Basic)=\dfrac{3x}{6x}=\dfrac{1}{2}$

(a)X=Monthly fee paid by a randomly selected customer.

Therefore, the probability distribution of X is given as:

$\left|\begin{array}{c|c}X&P(X)\\---&---\\\ 24.95&3/6\\\ 30.95&2/6\\\ 40.95&1/6\end{array}\right|$

(b)Average Monthly Revenue per customer

Mean,

$\mu=(\ 24.95 \times 3/6)+(\ 30.95 \times 2/6)+(\ 40.95 \times 1/6)\\=\ 29.62$

(c)Standard Deviation

$\left|\begin{array}{c|c|c|c|c}x&P(x)&x-\mu &(x-\mu)^2&(x-\mu)^2P(x)\\-----&-----&----&----&-----\\\ 24.95&3/6&-4.67&21.8089&10.9045\\\ 30.95&2/6&1.33&1.7689&0.5896\\\ 40.95&1/6&11.33&128.3689&21.3948\\-----&-----&----&----&-----\\&&&&32.8889\end{array}\right|$

$\text{Standard Deviation}=\sqrt{(x-\mu)^2P(x)}\\=\sqrt{32.8889} \\ \sigma=\ 5.73$