Working of a problem--I have found the mean, variance and the standard deviation from the following info:
The probability that a cellular phone company Kiosk sells X number of new phone contracts per day is shown below----
X=4, 5, 6, 8, 10
P(X)=0.4, 0.3, 0.1, 0.15, .0.05
Mean=5.4
Variance=2.94
Standard deviation=1.71
Cool with this--question--what is the probability that they will sell 6 or more contracts three days in a row??
How do I set this up?
Z = (score - mean)/SD = (6-5.4)/1.71 = .6/1.71 = .35
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.
Since the probability that all events will occur is the product of the individual events, that proportion cubed is your answer.
This is familiar to me--the answer from my book is 0.027. ????
To calculate the probability of selling 6 or more contracts for three consecutive days, you can use the concept of independent events and the probability distribution you have.
Here's how you can set it up:
1. Calculate the probability of selling 6 or more contracts on a single day:
P(X ≥ 6) = P(X = 6) + P(X = 8) + P(X = 10)
= 0.1 + 0.15 + 0.05
= 0.3
2. Since the events are independent, the probability of selling 6 or more contracts for three consecutive days is the product of the probabilities for each day:
P(6 or more contracts for three consecutive days) = (P(X ≥ 6))^3
= 0.3^3
= 0.027
Therefore, there is a 0.027 (or 2.7%) probability that the company will sell 6 or more contracts for three days in a row.
To find the probability that the company will sell 6 or more contracts three days in a row, we need to calculate the probability of selling 6 or more contracts on each day and then multiply them together for three days.
To set up the calculation, follow these steps:
1. Identify the probability values for selling 6 or more contracts on each day. In this case, we need the probabilities for X = 6, 8, and 10.
2. Add up the probabilities for each day to find the cumulative probability. Since the probabilities are given for each value of X, simply add the probabilities for X = 6, X = 8, and X = 10:
P(X ≥ 6) = P(X = 6) + P(X = 8) + P(X = 10).
In this example, P(X = 6) = 0.1, P(X = 8) = 0.15, and P(X = 10) = 0.05:
P(X ≥ 6) = 0.1 + 0.15 + 0.05 = 0.3.
3. Since we are looking for the probability of selling 6 or more contracts three days in a row, we need to multiply the cumulative probability for one day by itself three times:
P(selling 6 or more contracts for three days) = P(X ≥ 6)^3.
In this example, P(X ≥ 6) = 0.3:
P(selling 6 or more contracts for three days) = 0.3^3 = 0.027.
Therefore, there is a 0.027 probability that the company will sell 6 or more contracts three days in a row.