Answer to Question #175195 in Statistics and Probability for kmy

Question

1. The probability that a cellular phone company kiosk sells X number of new phone  contracts per day is shown below. Find the mean, variance, and standard deviation for  this probability distribution.  

X - 7 8 9 12 14 

P (X) - 0.4 0.3 0.15 0.1 0.05 

What is the probability that they will sell 9 or more contracts three days in a row?

2. A pizza shop owner determines the number of pizzas that are delivered each day. Find  the mean, variance, and standard deviation for the distribution shown. If the manager  stated that 23 pizzas were delivered on one day, do you think that this is a believable  claim?  

Number of pizzas  X - 12 18 15 13 20 

Probability  P(X) - 0.1 0.2 0.3 0.3 0.1

Answer 1

1. Mean: $\mu = \sum X \times P(X) = 7\times0.4+8\times0.3+9\times0.15+12\times0.1+14\times0.05=8.45$

Variance: $\sigma^2= (\sum X^2\times P(X))-\mu^2 = (7^2\times0.4+8^2\times0.3+9^2\times0.15+12^2\times0.1+14^2\times0.05) - 8.45^2 = 3.75$

Standard deviation: $\sigma= \sqrt{3.75}= 1.94$

Probability of selling 9 or more contracts: (0.15+0.1+0.05)³ = 0.027

2. Mean: $\mu = \sum X \times P(X) = 12\times0.1+18\times0.2+15\times0.3+13\times0.3+20\times0.1 = 15.2$

Variance: $\sigma^2= (\sum X^2\times P(X))-\mu^2 = (12^2\times0.1+18^2\times0.2+15^2\times0.3+13^2\times0.3+20^2\times0.1)-15.2^2 = 6.36$

Standard deviation: $\sigma= \sqrt{6.36}=2.52$

It is unbielivable claim, as it is delivered $15.2\pm2.52$ pizzas daily