A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 69 customers. The dealer will be fined if the number of customers who report favorably is between 40 and 46. The dealership will be dissolved if fewer than 40 customers report favorably. It is known that 73% of the dealer’s customers report favorably on satisfaction surveys. a. What is the probability that the dealer will be fined? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)b. What is the probability that the dealership will be dissolved? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)
Answers
Step-by-step explanation:
The probability that the dealer will be fined is 0.0948
To find p(a <= Z <= b) = F(b) - F(a)
P(X < 20) = (20 - 30.5)/3.4489
= -10.5/3.4489
= -3.0444
= P(Z < -3.0444) from standard normal table
= 0.00117
P(X < 26) = (26 - 30.5)/3.4489
= -4.5/3.4489 = -1.3048
= P(Z < -1.3048) From standard normal table
= 0.09599
P(20 < x < 26) = 0.09599 - 0.00117 = 0.0948
The answer in this question is 0.0948
Final answer:
To determine the probabilities requested, the normal distribution model is employed. The number of favorable reports follows a normal distribution with mean μ = 0.73 * 69 and standard deviation σ. The probabilities are then calculated from the z-scores corresponding to the given ranges, using standard normal distribution tables or calculators.
Explanation:
To calculate the probability that the dealership will be fined or dissolved, we use the normal distribution model because the sample size is large enough, and the variable (the number of customers who report favorably) can be approximated by a normal distribution. Given that 73% of the dealer's customers report favorably, and we have a sample size of 69 customers, we can find the mean (μ) and the standard deviation (σ) of the distribution. The mean (μ) is 0.73 * 69, and the standard deviation (σ) is .
To find the z-score for the number of favorable reports between 40 and 46, we use the formula z = (x - μ) / σ. Then we find the corresponding probabilities using the standard normal distribution table or a calculator providing such functionalities. To find the probability that the dealer will be fined, we subtract the cumulative probability at the lower boundary from that at the upper boundary. Similarly, to find the probability that the dealership will be dissolved (fewer than 40 favorable reports), we find the cumulative probability at 39 (since it's fewer than 40) and use it directly because it represents all values below that number.
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Answers
-- Profit = (Retail price) minus (Wholesale price)
-- Wholesale price = (Retail price) minus (Profit)
-- Retail Price = (Wholesale price) plus (Profit)
-- English money works just like US money: £1.00 = 100p
Answers
Answer:
The cab is -1/3 west of north.
( from the starting point it goes 1 block to the north and 3 blocks to the west . Cab is at (-2,-1))
Step-by-step explanation:
It is given that:
A taxicab starts at (1, -2) on the grid.
- It goes 4 blocks south and 3 blocks east to pick up a passenger.
This implies that the cab will reach at a point (4,-6)
( Since going south means it will go some units down and similarly going east means it will go some units to the right.
Hence, here going 4 blocks south and 3 blocks east means it will go to:
(1,-2) → (1+3,-2-4)=(4,-6) )
- Then it goes 6 blocks west and 5 blocks north and drops off the passenger.
This means that the cab will drop the passenger at (-2,-1)
Since going north means it will go some units up and similarly going west means it will go some units to the left.
Hence, here going 6 blocks west and 5 blocks north means it will go to:
(4,-6) → (4-6,-6+5)=(-2,-1) )
Hence, the end point is (-2,-1)
Now the slope of the line joining the starting and the end point is:
i.e. line joining (1,-2) and (-2,-1) is:
Hence, the taxicab is -1/3 block west of north.
i.e. from the starting point it goes 1 block to the north and 3 blocks to the west.
i.e. the cab is in west-north direction from the starting point.
Answer:
3 Blocks west, 1 block north
Step-by-step explanation:
Answers
We need to express the ksp expression of C2D3
C2D3
= (2x)2(3x)3
= 108x5
Then set that equation equal to your solubility constant
9.14x10-9 = 108x5
x = 9.67x10-3
So the molar solubility is 9.67x10-3
or false?
Answers
Answer:
True
Step-by-step explanation:
Answer:
it really just depends
Step-by-step explanation:
Answers
Answer:
- slope = 3/2
- y-intercept = 3
- x-intercept = -2
Step-by-step explanation:
The slope is the coefficient of x when the equation is of the form ...
y = (something).
Here, we can put the equation in that form by subtracting 12x and dividing by the coefficient of y:
12x -8y = -24 . . . . . given
-8y = -12x -24 . . . . .subtract 12x
y = 3/2x +3 . . . . . . . divide by -8
This is the "slope-intercept" form of the equation. Generically, it is written ...
y = mx + b . . . . . . where m is the slope and b is the y-intercept
So, the above equation answers two of your questions:
slope = 3/2
y-intercept = 3
__
The x-intercept is found fairly easily from the original equation by setting y=0:
12x = -24
x = -24/12 = -2 . . . . . the x-intercept
_____
A graph of the equation can also show you these things. The graph shows a rise of 3 units for a run of 2, so the slope is rise/run = 3/2. The line crosses the axes at x=-2 and y=3, the intercepts.
Answers
Answer:
a matrix with 1's in the main diagonal and zeros everywhere. The identity matrix of order 2×2 is: [1 0 0 1].
Final answer:
The 2x2 identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It serves as the multiplicative identity in matrix multiplication, leaving the original matrix unchanged when multiplied.
Explanation:
In mathematics, the 2x2 identity matrix, denoted by the symbol I or Id, is a square matrix containing elements that make it act as the multiplicative identity in matrix multiplication. Specifically, a 2x2 identity matrix is written as:
I = [1, 0; 0, 1]
Here, the numbers 1 are positioned on the main diagonal from the top-left to bottom-right (also termed as principal diagonal). The other elements, outside the main diagonal, are 0. This particular configuration results in special properties such as, when any matrix is multiplied by the identity matrix, the original matrix is unchanged. So, if we have a 2x2 matrix A, then multiplying by the identity gives AI = IA = A.
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