A monument outside city hall has dimensions as shown in the figure below. If one gallon of paint can cover 202 ft^2 , how many g
allons of paint must be bought in order to paint the monument? Assume that the base of the monument cannot be painted and that paint can be bought only by the gallon.
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Answer:
The probability is 0.0775
The expected value is 4.75 clubs
The standard deviation is 1.8875 clubs
Step-by-step explanation:
The variable X follows a binomial distribution, because we have n identical and independent events (19 cards) with a probability p of success and 1-p of fail (there is a probability of 1/4 to be club and 3/4 to be diamond, heart or spade). Then, the probability that x of the n cards are club is:
So, the probability P of drawing at least 8 clubs is:
P = P(8) + P(9) + P(10) + ... + P(18) + P(19)
Replacing, the values of x, from 8 to 19, on the equation above, we get:
P = 0.0775
Additionally, the expected value E(x) and standard deviationS(x) for this distribution is given by:
E(x)=np = 19(0.25) = 4.75