In a game of chance, a player spins a square spinner labelled 1, 2, 3, 4. The outcomes are equally likely. The player wins the amount of money shown in the table alongside, depending on which number comes up. (i) Construct a probability distribution table return for one spin (ii) Determine the expected return for one spin of the spinner (iii) Find the expected gain of the player if it costs $5 to play each game (iv) Determine whether you would recommend playing this game. Give a reason to support your recommendation.
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.
In a game of chance, a player spins a square spinner labelled 1, 2, 3, 4. The outcomes are equally likely. The player wins the amount of money shown in the table alongside, depending on which number comes up.
(i) Construct a
(ii) Determine the expected return for one spin of the spinner
(iii) Find the expected gain of the player if it costs $5 to play each game
(iv) Determine whether you would recommend playing this game. Give a reason to support your recommendation.
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