Question

A carnival game involves a spinner that is designed so that in 20 percent of spins the player will win a prize. A random sample of 100 spins will be observed and the random variable X = number of times in the sample that the player won a price will be recorded. For the questions below, consider the process of finding the indicated probability by using the normal distribution as an approximation, including making the appropriate continuity correction. (Note that you are only being asked to compute the appropriate z-scores.)

(a) To find the probability that X will be more than 28, you would compute z = .

(b) To find the probability that X will be less than 19, you would compute z = .

(c) To find the probability that X will be at least 20, you would compute z = .

(d) To find the probability that X will be at most 21, you would compute z = .

Answer #1

a) The probability that X will be more than 28 is

b) The probability that X will be less than 19 is

c)

The probability that X will be at least 20 is

d) The probability that X will be at most 21 is

A player spins two spinners. The outcome of each spinner is 1,
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variable that denotes the maximum of the two numbers on the
spinners.
a. Find the distribution of X. That is, for each possible value
of X, say what is the probability X would get that value.
b. What is E(X)?

A game is played in which you spin a 10-segment spinner as shown
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below.
(a) Find the probability that you spin 4:
P(spin 4) = (round to one decimal place)
(b) Find the probability that you spin either 9 or 10:
P(spin 9 or 10) = (round to one decimal
place)
(c) X is a binomial random variable. Suppose we define spinning 9
or 10 as "success", and we decide...

X
P(X=x)
Geoff is running a carnival game. He has 15 marbles in a bag:
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play a round of the game, a player randomly takes out a marble from
the bag, notes the color and replaces it, then pulls a second
marble from the bag and notes the color. So in effect, the player
pulls 2 marbles from the bag. (However, the first marble is put
back...

You are trying to decide whether to play a carnival game that
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the number 1 comes up at all, you get your money back, and get $1
for each time it comes up. So for example if it came up twice, your
profit would be $2. The table below gives the probability of each
value for the random variable X, where:
X = profit from playing the...

You consider yourself a bit of an expert at playing
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any given game is 0.4. In a tournament that consists of playing 60
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the of number games won. Assume that the probability of winning a
game is independent of the results of previous games.
You should use the normal approximation to the binomial to
calculate the following probabilities. Give your...

Make a probability distribution function table for the game
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occurs, and P(x) is the probability that event x occurs. The
expected payoff (i.e., the amount you would win/lose on average per
play after playing the game many times) is E. Find E for the game
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There are 16 cards placed face down on a table. On the face
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1.A weekend TV game show called rolling a dice is running each
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a) (2 mark) Calculate the average earning of a
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b) Calculate the probability that ? ⩽ 2 (show your
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One day, a city's baseball team lost their 78th game of the
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Click the icon to view the...

Suppose x has a distribution with a mean of 20 and a standard
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Is the sampling distribution of x normal? How do you
know?
What is the mean and the standard deviation of the sampling
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Find the z score corresponding to x = 19.
Find P (x < 19).
Would if be unusual for a random sample of size 36 from the x
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True or False:
10. The probability of an event is a value which must be greater
than 0 and less than 1.
11. If events A and B are mutually exclusive, then P(A|B) is always
equal to zero.
12. Mutually exclusive events cannot be independent.
13. A classical probability measure is a probability assessment
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14. The probability of an event is the product of the probabilities
of the sample space outcomes that correspond to...

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