Answer:
Probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Step-by-step explanation:
We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.
<em>Let X = number of viewers for the American Idol television show</em>
So, X ~ N(
)
Now, the z score probability distribution is given by;
Z = 
~ N(0,1)
where, 
= population mean = 26 million
= standard deviation = 8 million
So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X 
30)
P(X < 37) = P( < 
) = P(Z < 1.38) = 0.91621
P(X 30) = P( 
) = P(Z 0.50) = 0.69146
<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>
Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.
The answer is :
c. (x+1)²=20
To check:
(x+1)²=20 (a+b)²=a²+2ab+b²
x²+2x+1=20
x²+2x=20-1
x²+2x=19
Answer:
a) 3.47% probability that there will be exactly 15 arrivals.
b) 58.31% probability that there are no more than 10 arrivals.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
If the mean number of arrivals is 10
This means that 
(a) that there will be exactly 15 arrivals?
This is P(X = 15). So
3.47% probability that there will be exactly 15 arrivals.
(b) no more than 10 arrivals?
This is 
58.31% probability that there are no more than 10 arrivals.
Answer:
Step-by-step explanation:
Multiplying a(x) and b(x) together results in a quadratic equation (a trinomial). This trinomial looks like (a·b)(x) = (2)(x - 2)(x + 2). Note that this is a "special product;" (2)(x^2 - 4); there is no middle term.
Answer:
A ≈ 269.81 cm²
Step-by-step explanation:
This shape is a hexagon (it has 6 sides) so let's use the formula for the area of a hexagon.
A = 
Where s is the length of the sides
Substitute:
A =
A = 
Solve:
A =
A = 
Multiply the numerator:
A =
A ≈ 
(The numerator reflects a rounded number, but the actual calculations are exact)
Divide the fraction:
A ≈
A ≈ 2.6(100)
Multiply:
A ≈ 2.6(100)
A ≈ 269.81 cm²
Therefore, the area is approximately 269.82 cubic centimeters.
