Answer:
The probability is 0.9909.
Step-by-step explanation:
Test statistic (z) = (sample mean - population mean) ÷ (sd/√n)
sample mean = 290 days
population mean = 298 days
sd = 22 days
n = 42
z = (290 - 298) ÷ (22/√42) = -8 ÷ 3.395 = -2.36
The cumulative area of the test statistic is the probability that the mean gestation period is less than 290 days. The cumulative area is 0.9909. Therefore the probability is 0.9909.
Answer:
16.05% probability of 6 job applications received in a given week.
Step-by-step explanation:
When you have the mean during an interval, you should use the Poisson distribution.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Records show that the average number of job applications received per week is 5.9.
This means that ![\mu = 5.9](https://tex.z-dn.net/?f=%5Cmu%20%3D%205.9)
Find the probability of 6 job applications received in a given week.
This is P(X = 6).
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 6) = \frac{e^{-5.9}*(5.9)^{6}}{(6)!} = 0.1605](https://tex.z-dn.net/?f=P%28X%20%3D%206%29%20%3D%20%5Cfrac%7Be%5E%7B-5.9%7D%2A%285.9%29%5E%7B6%7D%7D%7B%286%29%21%7D%20%3D%200.1605)
16.05% probability of 6 job applications received in a given week.
Answer:
the answer is A
Step-by-step explanation:
this this is because a is inversely proportional to b so therefore k becomes an inverse variation
Answer:
![p(q(x)) = 2x^2 - 16x + 30](https://tex.z-dn.net/?f=p%28q%28x%29%29%20%3D%202x%5E2%20-%2016x%20%2B%2030)
Step-by-step explanation:
The notation (p•q)(x) means p(q(x)) or p of q of x. To find it, substitute q(x) into p(x) and simplify:
![p(q(x)) = 2(x-3)^2 - 4(x-3)\\p(q(x))=2(x^2-6x+9) - 4x + 12\\p(q(x)) = 2x^2-12x+18-4x+12\\p(q(x)) = 2x^2 - 16x + 30](https://tex.z-dn.net/?f=p%28q%28x%29%29%20%3D%202%28x-3%29%5E2%20-%204%28x-3%29%5C%5Cp%28q%28x%29%29%3D2%28x%5E2-6x%2B9%29%20-%204x%20%2B%2012%5C%5Cp%28q%28x%29%29%20%3D%202x%5E2-12x%2B18-4x%2B12%5C%5Cp%28q%28x%29%29%20%3D%202x%5E2%20-%2016x%20%2B%2030)