Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with P(A) = 0.4, P(B) = 0.2, and P(C) = 0.4. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? mean customers variance customers2 Explain your reasoning. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X = the probability that a customer used a debit card.Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X = the number of customers who use a debit card. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X = the number of customers at the gas station. (b) Answer part (a) for the number among the 100 who don't pay with cash. mean customers variance customers2
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with P(A) = 0.4, P(B) = 0.2, and P(C) = 0.4.
| mean | customers |
| variance | customers2 |
Explain your reasoning.
(b) Answer part (a) for the number among the 100 who don't pay with cash.
| mean | customers |
| variance | customers2 |
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