A car salesman is stringing banners from the top of the roof to a fence pole 20 feet away. The top of the roof is 29 feet from t
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Answer:
a) The distribution for the random variable X is given by:
X | -5 | 95 | 745 | 1995 |
P(X) | 6992/7000 | 5/7000 | 2/7000 | 1/7000 |
b) E(X)=-4.43. That means if we buy an individual ticket by $5 on this lottery the expected value of loss if $4.43.
c)
Step-by-step explanation:
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
Part a
The info given is:
N=7000 represent the number of tickets sold
$5 is the price for any ticket
Number of tickets with a prize of $2000 =1
Number of tickets with a prize of $750=2
Number of tickets with a prize of $100=5
Let X represent the random variable net gain when we buy an individual ticket. The possible values that X can assume are:
___________________________
Ticket price Prize Net gain (X)
___________________________
5 2000 1995
5 750 745
5 100 95
5 0 -5
___________________________
Now we can find the probability for each value of X
P(X=1995)=1/7000, since we ave just one prize of $2000
P(X=745)=2/7000, since we have two prizes of $750
P(X=95)=5/7000, since we have 5 prizes of $100
P(X=-5)=6992/7000. since we have 6992 prizes of $0.
So then the random variable is given by this table
X | -5 | 95 | 745 | 1995 |
P(X) | 6992/7000 | 5/7000 | 2/7000 | 1/7000 |
Part b
In order to calculate the expected value we can use the following formula:
And if we use the values obtained we got:
That means if we buy an individual ticket by $5 on this lottery the expected value of loss if $4.43.
Part c
In order to find the standard deviation we need to find first the second moment, given by :
And using the formula we got:
Then we can find the variance with the following formula:
And then the standard deviation would be given by:
Answer:
The cost of a bag of chips is
Step-by-step explanation:
Let
c ----> the cost of a bag of chips
we know that
The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05
The cost of 3 bags of chips is equal to multiply 3 by its cost c
so
The linear equation that represent this situation is
solve for c
Subtract 2.50 both sides
Divide by 3 both sides