As you can see, Sessa's request is the powers of 2, starting at 0. Question: On which day should Sesa have expected to receive 2, 048 grains of rice ?
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.
Sessa, an ancient wise man, visited the king of his nation and showed him a new game. The board was 8 squares by 8 squares. Two players would be given 16 pieces each, lined up on either side of the board. The pieces moved in set ways, and the purpose of the game was to move your pieces to trap the King piece of the other player.
As you have probably figured out, Sessa invented chess.
His king was utterly delighted at the game - war without bloodshed! - and asked Sessa what he would like in return. In the ancient bombastic style, the King said the request could include up to half of his kingdom. (That was not meant literally.) Sessa asked for the game board to be brought before him.
"Highness," he said, "I ask for a grain of rice on the first square. Tomorrow, two grains of rice on the second square. The day after, 4 grains of rice on the third square. On the fourth day, 8 grains of rice. And so on, until the board is full in two months."
The king and his ministers laughed uproariously at such a silly request. A few grains of rice from the king? Easily done! The king bade his ministers to do it, and Sessa was sent on his way with his grain of rice.
A few days later, the ministers came before the king, nervous and trembling. "Highness," one minister croaked out, his throat parched, "we cannot fulfill Sessa's request."
"WHAT?!?" Kings ruled by their hospitality. Heaven gave gifts to the king, and the king passed gifts to the people. If the kings were ungenerous or poor, that meant that they no longer enjoyed the blessing of heaven. If so, the king would lose the respect and prestige of his people, and he would need to guard his throat carefully.
"Bring a sack of rice!" roared the king. One was brought, and the king began to place the rice on the board. But after the first few squares, the king realized that his ministers were right. All the rice in the kingdom - all the rice ever grown under heaven - could not fill Sessa's request. The king called Sessa before him, debating whether to crown him or behead him.
"I cannot fulfill your request," the king admitted. "I am undone and will be cast from my throne and chased from the land. I beg forgiveness."
The king nodded to his guards, who understood. Sessa, wisest of men, understood as well. Sessa could accept the apology or visit his ancestors. The king continued.
"Since I cannot fulfill your request, you shall join me as Prime Minister. We will not speak of this incident."
Sessa bowed deeply. "Highness, if you wish it, I shall do it. But the ministry is too much work for my studies. I ask instead to be allowed to study and increase my wisdom, your wisdom, and the wisdom of this kingdom. I shall not, of course, mention this incident."
The king smiled broadly, and Sessa was made the chief of the king's wise men. With the king's blessing and funds, Sessa studied astronomy, mathematics, magic, and agriculture, and built a library to rival any in Asia. His wisdom, and the king's willingness to listen, soon made the kingdom prosperous. Sessa became a wealthy man, married three beautiful wives, sired 14 children, and lived to a pleasant old age of 94. He slept with his fathers.
In his honor, the game of chess took his name.
As you can see, Sessa's request is the powers of 2, starting at 0.
Question: On which day should Sesa have expected to receive 2, 048 grains of rice ?
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