There are 9 playing cards in a bag. Three cards have \"4\" on them, two cards ha
ID: 3206574 • Letter: T
Question
There are 9 playing cards in a bag. Three cards have "4" on them, two cards have "5" on them, three cards have "8" on them and one card has "10" on it. You randomly pull one card out of the bag. The random variable. X, represents the value on the card that you pulled out of the bag. What is the probability distribution of this situation? What is the probability that the value of a randomly chosen card is less than 8? Lunch prices for at local restaurants are normally distributed. The lunch price has a mean of $11.50 and a standard deviation of $2.00. If you choose a random lunch, what is the probability that the price is between $8.00 and $1400? If you choose a random lunch, you have a 0.209 probability of the price being less than what amount?Explanation / Answer
Q8.
Number
Frequency
4
3
5
2
8
3
10
1
( a )
Probability Distribution:
x
p ( x )
4
0.33
5
0.22
8
0.33
10
0.11
( b )
P ( less than 8 ) = P ( 4 ) + P ( 5 ) = 0.33 + 0.22 = 0.55
Answer: 0.55
Q9.
Mean = 11.5
SD = 2
( a ) P ( 8 < x < 14 )
z = ( x – Mean ) / SD
z-score for 8 = ( 8 – 11.5) / 2 = -1.75
z-score for 14 = (14 – 11.5)/2 = 1.25
P ( -1.75 < z < 1.25 )
= P ( z < 1.25 ) – P ( z < -1.75 )
P ( z < 1.25 ) = 0.8944
P ( z < -1.75 ) = 0.0401
P ( z < 1.25 ) – P ( z < -1.75 )
= 0.8944 – 0.0401
= 0.8543
Answer: 0.8543
( b )
Here first we find the z-score for P ( Z < z ) = 0.209
By using Normal Distribution Table we get,
P ( Z < -0.81) = 0.209
X = Mean + ( z * SD)
= 11.50 – (0.81*2)
= 9.88
Answer: 9.88
Number
Frequency
4
3
5
2
8
3
10
1
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