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The following diagram shows the curve of the normal distribution of the random variable X.
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The area of the shaded region R is 0.32.
Find the value of P(X<92).
It is given that P(X>58)=0.68.
Find the expected value, μ, of X.
Determine the value of
P(58<X<μ),
P(58<X<92∣X<92)
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The probability distribution of a discrete random variable X is shown in the following table.
Find the possible value(s) of p.
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At a local carnival, players can pay 6 tokens to play Lucky Spinner. Each turn, the player spins a wheel with segments numbered 0-4. If the wheel lands on s, the player wins s2 tokens.
The following table shows the distribution S of spins s.
It is given that the game is fair.
Show that a=2512​.
Find the value of b.
Let L∼B(5,p) be the random variable representing the number times a player loses money in 5 turns.
Show that p=12562​.
Find the variance of L, giving your answer to 4 decimal places.
Given that Elise lost money on at least 3 of her 5 turns, find the probability she lost money every time.
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