Answer:
A) probability of failure in next 100 hours given that it has been tested for 500 hours without failure is 0.181
B) probability that exactly two have the metabolic defect is 0.03
Step-by-step explanation:
Part A)
Let X be a exponentially random variable with mean = μ = 500 hrs
For exponential distribution:
λ = 1/μ
λ = 0.002
We have to find the probability of failure in the next 100 hours given that assembly has been tested for 500 hours without a failure.
Using memory less property of exponential distribution:
using
<h3>Part B)</h3>
Chances of occurrence of metabolic defect = 5%
P(C) = .05
No. of randomly selected infants = n =6
We have to find the probability that exactly two have the metabolic defect
⇒x = 2
Using binomial probability density function:
P = ![P=\left[\begin{array}{ccc}n\\x\end{array}\right] p^{x} (1-p) ^{n-x}\\\\=\frac{n!}{x!(n-x)!} p^{x} (1-p) ^{n-x}\\=\frac{6!}{2!4!}(.05)^{2}(.95)^{4}\\= 0.03\\](https://tex.z-dn.net/?f=P%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dn%5C%5Cx%5Cend%7Barray%7D%5Cright%5D%20p%5E%7Bx%7D%20%281-p%29%20%5E%7Bn-x%7D%5C%5C%5C%5C%3D%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D%20p%5E%7Bx%7D%20%281-p%29%20%5E%7Bn-x%7D%5C%5C%3D%5Cfrac%7B6%21%7D%7B2%214%21%7D%28.05%29%5E%7B2%7D%28.95%29%5E%7B4%7D%5C%5C%3D%200.03%5C%5C)
probability that exactly two have the metabolic defect is 0.03
Answer:
I think it is c too :))))))))
She worked 9 hours at baby-sitting and 6 hours at her parents store.
Step-by-step explanation:
Let,
Baby-sitting hours = x
Hours at parents store = y
Total hours = 15
Amount earned = $93
According to given statement;
x+y=15 Eqn 1
5x+8y=93 Eqn 2
Multiplying Eqn 1 by 5;
Subtracting Eqn 3 from Eqn 2;
Dividing both sides by 3;
Putting y=6 in Eqn 1
She worked 9 hours at baby-sitting and 6 hours at her parents store.
Keywords: linear equations, subtraction
Learn more about linear equations at:
#LearnwithBrainly
X - the total number of pages
There are 512 pages in the novel.
Answer:
a)
Mean = sum of all numbers in dataset / total number in dataset
Mean = 8130/15 = 542
Median:
The median is also the number that is halfway into the set.
For median, we need to sort the data and then find the middle number which in our case is 546. Below is the sorted data
486 516 523 523 529 534 538 546 548 551 552 558 566 574 586
Standard Deviation (SD). Here X represents dataset and N= count of numbers in data
As per the SD formula, which is Sqrt ( sum (X_i - Meanx(X))/(N-1))
SD= 25.082
2) Formula for coefficient of skewness using Pearson's method (using median) is,
SK = 3* ( Mean (X) - Median(X))/(Standard Deviation) = 3*(542-546)/25.082 = -0.325
3) coefficient of skewness using the software method is also same which is -0.325
