What is the volume of this pyramid? 945 cm³ 1260 cm³ 1890 cm³ 2520 cm³ A pyramid with a right triangular base. The right triangu
2 answers:
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This is a problem on hypothesis testing on the difference of two dependent means. To solve for this one, the difference for each pair should be solved.
After it, the mean and standard deviation of the differences should also be calculated. Then, we state the null and alternative hypotheses.
The null hypothesis is
The alternative hypothesis is
These are the required hypotheses <span>to see whether the number of graffiti incidents declined. </span>
After it, the mean and standard deviation of the differences should also be calculated. Then, we state the null and alternative hypotheses.
The null hypothesis is
The alternative hypothesis is
These are the required hypotheses <span>to see whether the number of graffiti incidents declined. </span>
Answer:
(a) 0.4096
(b) 0.64
(c) 0.7942
Step-by-step explanation:
The probability that the player wins is,
Then the probability that the player losses is,
The player is playing the video game with 4 different opponents.
It is provided that when the player is defeated by an opponent the game ends.
All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)
(a)
The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.
The probability that the player defeats all four opponents in a game is,
P (Player defeats all 4 opponents) =
Thus, the probability that the player defeats all four opponents in a game is 0.4096.
(b)
The probability that the player defeats at least two opponents in a game is,
P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) =
Thus, the probability that the player defeats at least two opponents in a game is 0.64.
(c)
Let <em>X</em> = number of times the player defeats all 4 opponents.
The probability that the player defeats all four opponents in a game is,
P(WWWW) = 0.4096.
Then the random variable
The probability distribution of binomial is:
The probability that the player defeats all the 4 opponents at least once is,
P (<em>X</em> ≥ 1) = 1 - P (<em>X</em> < 1)
= 1 - P (<em>X</em> = 0)
Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.